Citation
Acoustic fundamentals of recording environments

Material Information

Title:
Acoustic fundamentals of recording environments
Creator:
Hicks, Daniel A
Place of Publication:
Denver, Colo.
Publisher:
University of Colorado Denver
Publication Date:
Language:
English
Physical Description:
viii, 163 leaves : illustrations ; 28 cm

Thesis/Dissertation Information

Degree:
Master's ( Master of Science)
Degree Grantor:
University of Colorado Denver
Degree Divisions:
Department of Music and Entertainment Industry Studies, CU Denver
Degree Disciplines:
Recording Arts
Committee Chair:
Pritts, Roy
Committee Members:
Sanders, Rich
Krantz, Richard

Subjects

Subjects / Keywords:
Sound -- Recording and reproducing ( lcsh )
Sound studios ( lcsh )
Sound recordings -- Production and direction ( lcsh )
Sound -- Recording and reproducing ( fast )
Sound recordings -- Production and direction ( fast )
Sound studios ( fast )
Genre:
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Bibliography:
Includes bibliographical references (leaves 161-163).
General Note:
College of Arts and Media
Statement of Responsibility:
by Daniel A. Hicks.

Record Information

Source Institution:
|University of Colorado Denver
Holding Location:
|Auraria Library
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
74820541 ( OCLC )
ocm74820541
Classification:
LD1193.A78 2006m H52 ( lcc )

Full Text
ACOUSTIC FUNDAMENTALS OF RECORDING ENVIRONMENTS
by
A course proposed to the
University of Colorado at Denver and Health Sciences Center
College of Arts and Media, Music and Entertainment Industry Studies
in partial fulfillment
of the requirements of the degree of
Master of Science
Recording Arts
Daniel A. Hicks
B.S., Michigan Technological University, 2002
M.S., Michigan Technological University, 2003
2006


This project portfolio for the Master of Science
degree by
Daniel A. Hicks
has been approved
by
Roy Pritts
$//lJ 0&
>ate


Hicks, Daniel A. (M.S.R.A., University of Colorado at Denver and Health Sciences
Center)
Acoustic Fundamentals of Recording Environments
Project portfolio directed by Professor Roy Pritts
ABSTRACT
Room acoustics profoundly affect the quality of any sound signal that is
conveyed in that room. Room acoustics will often dictate the difference between what
is recorded and what a recording engineer thought was recorded, as well as, play a
major role in the decisions an engineer will make during mixing. A properly designed
critical listening space is crucial for professional mixing and recording situations. For
these reasons, all serious recording engineers should learn the fundamentals of
recording acoustics.
Unfortunately, because they are a relatively new development in academia, I
have found that the majority of technical and university level recording arts
institutions do not include acoustics in their curriculum. Existing literature and
textbooks that cover the scope of recording acoustics are either too scientific and
require a deep understanding in advanced mathematics and calculus from the reader,
or are too practical, solving acoustical dilemmas using consumer products and
without discussing underlying principles of the solution. For an appropriate education


in the fundamentals of acoustics, students should understand acoustic principles as
well as be able to apply them to real world problems in the form of acoustical
solutions.
My approach is to develop a course focusing on acoustics of recording
environments for undergraduate recording arts students. This course will cover both
the fundamentals required for understanding in a basic level acoustics course and
approaches to solve real world acoustic problems. The course is structured for a
fifteen-week semester with one additional week for a final exam. The course structure
makes use of PowerPoint, listening examples, quizzes, homework, exams, and a final
project.
This abstract accurately represents the content of the candidates portfolio. I
recommend its publication.
Signed
Roy Pritts


ACKNOWLEDGEMENT
I would like to start by thanking my project advisor, Roy Pritts, and the
members of my committee, Rich Sanders and Dr. Richard Krantz, for their efforts to
help me in the progression of this project. They are all a great source of information,
ideas, and help. I would also like to thank John Storyk for inspiring me to create this
course and presenting his Architecture and Acoustics of Critical Listening
Environments lecture series at the University of Colorado at Denver.
I would like to recognize my friends and family in Denver and at Auraria
who have and continue to make my educational journey exciting, memorable, and
alive with opportunities and friendships. I would especially like to thank the staff at
GLBTSS at Auraria for providing me with a space on campus to work on this project.
Lastly, I would like to thank my parents and family for their support. They
have helped support me with moving across the country in pursuing this degree and
have always been there for me when I needed them.


CONTENTS
Chapter
1. Introduction and Scope.................................................1
1.1 The Importance of Proper Acoustics....................................1
1.2 The Critical Listening and Performance Environment....................2
2. Current Education in Acoustics.........................................3
2.1 Existing Courses......................................................4
2.2 Existing Literature..................................................5
2.2.1 Musical Acoustics...................................................5
2.2.2 Scientific and Architectural Acoustics..............................6
2.2.3 Practical Acoustics.................................................6
3. Course Development.....................................................8
3.1 Constraints in Teaching...............................................8
3.1.1 Relation to Other Departmental Courses..............................9
3.1.2 Course Necessities..................................................10
3.1.3 Content and Non-content Goals.......................................10
3.2 Textbook Selection...................................................11
3.2.1 Supplementary Reading Materials.....................................11
3.3 Course Syllabus......................................................11
3.3.1 Topics Covered......................................................12
3.3.2 Homework............................................................13
vi


3.3.3 Exams
13
3.3.4 Quizzes.........................................................14
3.3.5 Final Project...................................................14
3.4 Course Website....................................................15
3.5 Suggested Class Activities........................................16
4. Detailed Lesson Plans..............................................17
4.1 Course Introduction and Homework 1................................18
4.2 Math Review and Homework 2........................................24
4.3 Sound Waves and Homework 3........................................35
4.4 Psychoacoustics and Homework 4....................................43
4.5 Acoustic Measurements and Homework 5..............................49
4.6 Isolation Acoustics and Homework 6................................65
4.7 Internal Acoustics and Homework 7.................................85
4.8 Starting to Design and Homework 8.................................104
4.9 Studio Design and Homework 9......................................109
4.10 Control Room Design and Homework 10.............................115
4.11 Performance Space Design and Homework 11........................123
4.12 Exams...........................................................129
4.13 Final Project...................................................129
5. Future Course Additions............................................130
5.1 Software..........................................................130
Vll


Appendix
A. Surveyed Textbooks................................................131
B. Content and Non-content Goals.....................................135
C. Textbook and Supplementary Reading Materials......................139
D. Course Syllabus...................................................141
E. Quizzes...........................................................146
F. Mid-Term Exam.....................................................148
G. Final Exam........................................................153
H. Final Project.....................................................156
I. Acoustic Measurement Software......................................160
Bibliography..........................................................161
VUl


1. Chapter Introduction
The acoustics of a room profoundly affect the sound signal that is conveyed in
that room. They will often dictate the difference between what is recorded, what the
recording engineer thought was recorded, and the decisions that will be made during
the mixing process. All serious recording engineers should learn the fundamentals of
recording acoustics but, for a variety of reasons, this is rarely taught in recording arts
programs. A properly designed critical listening space is necessary for professional
recording.
The skills necessary to create such a recording environment arent difficult to
grasp but do require basic knowledge of math and algebra, sound wave propagation,
and psychoacoustics. The topics taught in such a course should cover isolation
acoustics, internal acoustics, design planning, and take a specific look at studios,
control rooms, and performance halls.
1.1 The Importance of Proper Acoustics
A critical listening space is crucial for a professional recording. Without an
appropriate environment for an engineer to listen to their recording, they will not be
able to make appropriate decisions about the content of the recording. This is also
true for the studio and performance space. If a musician cannot hear what they are
playing in the studio with appropriate clarity and feeling, they will not play to their
full potential and the recording will suffer.
1


With proper knowledge, a critical listening and performance environment can
be created to give the recording engineer a professional space to work.
1.2 The Critical Listening and Performance Environment
To understand what is needed for a critical listening and performance
environment a basic understanding of math, algebra, sound wave propagation, and
psychoacoustics is needed. Armed with these tools a student can more deeply
understand the acoustics necessary for a critical listening and performance space.
The acoustics of such environments can be split up into two major subjects:
Isolation acoustics and internal acoustics. Isolation acoustics involve the transmission
of sound through structures, walls, and between rooms. Internal acoustics involves the
control of sound in a particular space, its reflections and absorption, and the
characteristics of sound that are recorded or heard by an audience.
2


2. Chapter Current Education in Acoustics
The current state of education in acoustics as it relates to the recording arts
curriculum is unique. Technical and university level recording arts institutions
themselves are a relatively new field of study within academia. In my personal survey
of a few such programs, the acoustics courses taught often exclusively borrow from
other departments that deal with more classical acoustics study such as architecture
and psychoacoustics.
The modem recording industry is also shaping the way the recording arts
curriculum is being taught and this gives a unique perspective on the subject of
acoustics. No longer does music have to be recorded in large recording studios. With
the advent of digital recording and new technologies, the recording studio has
changed from a large, professional facility to a space that can occupy the home
basement or spare bedroom. Because of this, there is a real need for acoustic
education as it pertains to what is really happening in the recording world today in
modem, relatively small studio environments. These skills can then be easily applied
to larger, classic recording environments.
I offer a new type of acoustics course, the acoustics of recording
environments, as a course offering that may be of interest to those students who are
interested in the recording arts and for addition to existing recording arts curricula.
3


2.1 Existing Courses
The existing courses taught to recording arts majors in acoustics are often
general education courses that are borrowed from another departments curriculum.
Typically, the courses offered are musical acoustics and physics of sound,
psychoacoustics, and architectural acoustics.
Musical acoustics and physics of sound courses are those that look at the way
instruments create different tones, how musical scales are built, and the complex
ways sound combines to create timbre. They typically arent concerned with acoustic
spaces or listening environments.
Psychoacoustics also does not fully explore the design of acoustic spaces. For
example, the study of psychoacoustics will give meaning to the importance of early
reflections and will help the recording arts student understand the standards by which
monitors are setup in a control room. They dont, however, go far enough to explain
how to modify early reflections so that they do not interfere with appropriate mixing
decisions or how a monitor setup, although technically correct by the standard
recommendations, can be incorrectly set up for a specific listening space.
Architectural acoustics courses are, in fact, the best type of acoustics courses
available to the recording arts student with regards to critical listening and
performance space acoustics. The problem, however, is that they require the student
to have a background in architecture, advanced algebra, and calculus. Most students
who attend a recording arts curriculum do not have this type of background;
4


recording arts students are most often have a music background with a strong interest
in recording. Architectural acoustics, as it is normally taught, is too advanced in
physics and math for the typical recording arts student.
2.2 Existing Literature
Similar to the three major types of courses offered to recording arts students,
there are three main categories of literature offered to the student who wishes to
pursue an understanding of critical listening and performance environments: musical
acoustics and physics of sound texts, textbooks dealing with scientific and
architectural acoustics, and handbooks surveying practical acoustics applications.
While these texts are important for their individualized fields of use, they are not
necessarily, in and of themselves, good teaching tools for a course in designing
critical listening spaces in recording environments.
2.2.1 Musical Acoustics
The musical acoustics and physics of sound text covers the components of
sound from particular instruments such as resonances in tubes, pipes and strings, the
harmonics and partials that compose the timbre of the instruments, and the interplay
of sounds that make up particular scales and modes. Occasionally, a musical acoustics
text will cover the relationship between the reverberation time of the performance
space and the type of music composed for that space as well as the placement of
5


instruments in an orchestra but they do not concern themselves with the proper design
of acoustic spaces.
These subjects are undoubtedly important to the musician but do not have
much relevance to the recording arts student who is concerned with recording arts
more than playing music or creating a new instrument.
2.2.2 Scientific and Architectural Acoustics Textbooks
The scientific and architectural acoustics textbooks are the classical textbooks
reserved for the architecture student. They are often very technical in nature and
require a good grasp of advanced mathematics and calculus. They are very thorough
in their scope. These textbooks, however, do not meet the needs of the recording arts
student because they assume that the student studies acoustics exclusively. They
provide too much depth of knowledge and assume too many prerequisites to be useful
or a practical teaching tool.
2.2.3 Practical Acoustics Handbooks
The texts that cover practical acoustics are most often intended for the
construction engineer in the field. They provide easy to use mathematical equations
but occasionally lack the background development that is needed for more serious
understanding of the subject. Some handbooks, however, are split up into sections to
serve different needs. One section will be focused on practical applications and
6


another on the theoretical background behind the practical applications. These types
of handbooks can be both a beneficial shortcut text for the engineer in the field as
well as a good teaching tool. They are also usually much less expensive than a
traditional textbook and provide something the student will find useful in class as
well as in the future to be used as a reference.
7


3. Chapter Course Development
My approach is to develop a recording acoustics course for undergraduate
recording arts students. This course will cover both the fundamentals required for
understanding in a basic level acoustics course as well as approaches to solve real
world acoustic problems. The course is structured for a fifteen-week semester with
one additional week for a final exam. The structure of the course uses PowerPoint,
listening examples, quizzes, homework, exams, and a final project.
3.1 Constraints in Teaching
While, initially, it may seem appropriate for an instructor to include as much
information as possible into a course on a particular subject, there are practical
restraints on the scope of the course that need to be addressed. The two most obvious
restraints are the course relationship to other courses in the department and the
specific goals of the course. If the course is out of line with the larger goals of the
department, the course will simply not be taught in that department. Because a
semester is a finite amount of time, the necessary goals of teaching such a course
need to be taken into account. After deciding the bare minimum of information
necessary in the course, the instructor can then try to incorporate more information as
needed.
8


3.1.1 Relation to Other Departmental Courses
A course may have one of three different roles within a larger department. It
may serve as an introduction for more advanced classes, be a general education
course to be used as exposure to non-majors, or it may be an advanced course for
majors. This course is structured to be used as an advanced course for recording arts
majors.
Understanding of the information in this course will allow the student to
pursue a more technical education if they desire. Even though this course is advanced
study for recording arts majors, it only encompasses a basic education in the design of
acoustic environments for recording applications. To make sure that all students will
be able to succeed in this course, the course has been designed to only require basic
math and high school algebra skills and will have a short review section built into its
curriculum to review math and physics concepts used in the rest of the course.
Because this is an advanced study course, only a limited amount of class time
is devoted to reviewing math and physics concepts. It may be beneficial to consider
requiring a general education physics course as a prerequisite to this course. This will
allow the student to engage the basic math and physics skills in a more in-depth
fashion. The beginning topics of this course will then become a review of what the
student has learned in prerequisite courses.
9


3.1.2 Course Necessities
There are only a few classroom necessities needed for the teaching of this
course. The course makes extensive use of PowerPoint as a teaching tool. The
classroom for this course, therefore, should have capabilities for a projector and a
projection screen. There are also several listening examples within the course lectures
which will require the use of computer that can connect to the computer.
In addition to the classroom necessities, the instructor should have available a
basic sound level meter as well as a measuring tape for demonstrations. Portable
acoustic measurement software for use on a computer, like SmaartLive, would also be
beneficial for in-class demonstrations. These types of software are further explored in
section 5.1.
3.1.3 Content and Non-content Goals
Both content and non-content goals should be identified before the
construction of a new course (Fuhrmann and Grasha, 1983). To do this, it is best to
start with a general list of requirements and then add specific details. Appendix B
contains two lists of content and non-content goals, their general requirements and
more detailed topics.
10


3.2 Textbook Selection
The textbook chosen for a course has a greater influence on what students
learn than the teaching method (McKeachie, 1986). It is important to find a textbook
that will relate to the course goals and outline.
I found that The Master Handbook of Acoustics, Fourth Edition by F. Alton
Everest is technical enough to be used as a textbook and has a broad enough scope to
cover all of the topics in the course. New copies of this book sell between $20 and
$30 and the text is also available in electronic Adobe PDF form. The book contains
chapters that talk both about theory and practical design applications.
3.2.1 Supplementary Reading Materials
An annotated list of supplementary books can be found in Appendix C.
Students will find that these books might be beneficial to read if they are looking for
more information on a specific interest. These books are common to most medium to
large sized libraries and may also be available through inter-library loan if the library
participates.
3.3 Course Syllabus
The syllabus is often the most formal communication tool for sharing
information about a course with students (Eberly, Newton, and Wiggins, 2001).
Because syllabi are used to communicate a formal contract of what is expected of
11


students, syllabus analysis is often the initial step taken when developing or
restructuring a course.
A successful syllabus should outline the topics of the course and the order
they will be studied, the reading for the course, homework, exams, class activities,
and everything else pertinent to the flow of the course through the semester. More
information is better than not enough information (Davis, 1993). It is also important
that the syllabus be flexible to allow for changes that will come up midway into the
semester due to unforeseen circumstances. To allow for these changes, the course
syllabus contains suggested activity days. It is advisable that the instructor tries to use
these scheduled days performing the suggested activities with the class but they can
be used as a cushion in the schedule if necessary.
3.3.1 Topics Covered
The topics I propose for this course meet the goal of teaching the
fundamentals of acoustic design as well as its underlying science. The major topics
for this course are:
Review of Mathematics and Graphs
Sound Waves and Propagation
Psychoacoustics
Acoustic Measurements
Isolation Acoustics
Internal Acoustics
First Steps of Design
Studios
Control Rooms
12


Large Halls and Performance Spaces
At the end of the last three lecture topics there is a slide presented for class
discussion as an opportunity for the class to discussion recording techniques inside of
studios, control rooms, and large performance spaces. This is a good time for the
instructor to tie the lecture topics back into the subject of recording and provide
listening examples and experiences as they see fit.
3.3.2 Homework
A reasonable amount of homework is often seen as an important part of
college life and can help both students and the instructor throughout the course.
Homework for this course will be assigned in class at the beginning of each new topic
and collected before class on the day of the next new topic. It will cover the major
points for the topic and should be done individually, although seeking help and
working in groups with other students is permissible. The main emphasis of the
homework is to get the student to engage the material and work to understand the
main concepts of the topic. Time will be allotted in the beginning of each class to
answer questions about the homework, if needed.
3.3.3 Exams
There will be two exams, one mid-term and one final, to test student
comprehension. The mid-term exam will cover the testable material from the first six
I
13


weeks. Because of the math and physics base of acoustics, these beginning weeks are
the foundational weeks covering the fundamentals needed to understand the concepts
in the final six weeks of class. The final exam will focus mainly on the final six
weeks of class but will be cumulative in the sense that it will ask students to draw
upon the fundamentals learned during the first six weeks. The instructor should also
consider placing additional questions on the final exam from class discussions or
previous homework that the students have found difficult or still need to review.
3.3.4 Quizzes
Quizzes will be unannounced and given throughout the semester for topics
three through seven. The benefit of using unannounced quizzes in class will be as an
incentive for the students to review class material outside of the classroom. It would
be easy for a student to meet in a group of other students and complete the homework
with marginal understanding, but the unannounced, in-class quiz will give that
student extra motivation to try and understand the topics more clearly and ask for help
if needed. Example quiz questions for this course can be found in Appendix E.
3.3.5 Final Project
The final project will be completed in groups of three or four students. Each
group will be presented with a scenario and a budget and will be asked to design a
small project studio. Everything discussed in the course should be considered in the
I
14


design recommendation. Time will be taken in class near the end of the semester for
the groups to meet and work as well as ask the instructor for help. Each group will
receive slightly different budgets and situations. Five suggested design scenarios can
be found in Appendix H.
The last three class periods will be devoted to presentations from the groups.
They will be asked to present their scenario, budget, and design solution. Each group
will be asked to write up a final project document outlining the specifics of their
project to be handed in during the last class of the semester.
3.4 Course Website
Students with access to both classroom lectures as well as an online classroom
environment perform better than students who only have access to classroom lectures
or internet courses (Wheeler and Jarobe, 2001). A web enhanced website that
contains the course syllabus, course content like homework sets and lecture notes,
links to material on the internet, and a student discussion board is very beneficial as a
supplement for traditional classroom lectures. Students can also check the progress of
their grades and notify the instructor if there is a grading discrepancy. Professional
software applications such as Blackboard Academic Suite can be used to create a
customized online environment to enhance student learning and most universities are
already offering the service to instructors who wish to use it.
15


3.5 Suggested Class Activities
The course outline provides scheduled time for suggested class activities such
as guest lectures from local architects or acousticians, listening and measurement
demonstrations, and class trips to local studios and concert halls. The instructor is
encouraged to try and use these activity days to let the students hear from
professionals in the field talk about real world problems that they encounter and
experience a connection between what is discussed in class and what really happens
in real life. These scheduled activity days allow the students a short break from
lectures and let them hear and experience activities that they normally wouldnt take
part in. If absolutely necessary, these days can be used as a cushion for restructuring
the course outline or to allow for days off due to instructor illness.
16


4. Chapter Detailed Lesson Plans
In this chapter, the lesson plans for each topic are outlined along with general
notes for classroom discussion. It is my intention to provide these lesson plans as a
skeleton that can be built upon with other discussions and exercises. They are, by no
means, a complete survey of the topic mentioned. They can be easily expanded upon
or shortened as the instructor feels necessary.
After each lesson plan, the appropriate homework set along with answers is
provided. The homework should be given at the end of the class period on the day of
the start of a new topic.
I have tried to provide the topics in a logical order so that each subsequent
topic builds upon the information gained from the previous topic while providing
more technical, detailed information. In this way, students engage the same material
multiple times and add deeper knowledge upon a subject at an easy pace.
Before starting new material each class period, time should be taken to answer
questions on the assigned homework. It is not advisable for the instructor to answer
questions directly off of the homework, but instead they should answer questions
about concepts and solve example problems as questions arise. After answering
homework questions, the previous days lecture can be quickly reviewed. This can be
easily accomplished using the provided PowerPoint slides as a guide.
17


4.1 Course Introduction and Homework 1
The course introduction topic introduces students to the outline of the course
and reviews the course syllabus. This topic covers the mechanics of the course such
as when homework will be assigned and collected, the dates of the exams and the
final project presentations, how students will be graded in the course, and how the
course topics are ordered in relation to the semester. The instructor should also
provide the course syllabus during this time for the students to review as the material
is being presented in class.
Homework 1 is designed to allow the instructor to learn more about the
students, learn the students names, as well as provide the students practice with the
required writing styles that will be necessary in the rest of the class, specifically on
the final project.
18


Introduction
Acoustic Fundamentals of Critical Listening and
Performance Spaces Topic 1 Introduction
Daniel Hicks
All pictures and images are creations of the author
unless otherwise specified.
Course Description
Room acoustics profoundly affect the signal that i* conveyed in that room. |
The purpose of this course will be to educate student. i
recording engineers with the fundamentals of recording I
acoustics so they wiU |
* be able to solve acoustical problems in existing places aid |
be able to properly design their own acoustic space |
I
i
____________________________________________________________i
It's important to understand how room acoustics
affect the sound conveyed in a space. With this
knowledge, engineers and performers will become
better at their craft
By the end of the course, students will be able to
solve acoustical problems in existing spaces and
design their own ideal space. This will allow them to
become better engineers and performers as well as
have a skill that many of their peers do not have.
Course Objectives
To provide a concrete understanding of
fundamental acoustic pnnciples
To develop problem solving skills and
apply them to real world projects
To team how to collaborate with other
engineenng professionals
Textbook
Master Handbook of Acoustics. Fourth
Edition by F Alton Everest.
ISBN: 0*07-136097-2
Available both in paperback and pdf formats
By the end of the course, students will imderstand the
basic pnnciples of acoustics, develop problem
solving skills that will allow them to use these
principles to solve real world problems, and
experience collaborating with other students and
professionals.
The course will not make students an expert on
acoustic spaces. It will give students a taste of the
field of acoustics and allow them to apply the basics
of acoustics successfully in real world applications.
Either format of textbook is acceptable. The
electronic version is not much cheaper than a new
paperbacL
19


i
Grading j
Final Project 100 points
Final Exam 80 points
Mid-Term Exam 80 points
Homework 110 points
Quizzes 50 points
Class Participation 30 points
Students grades will be based on the following point
system
Final project will be worth 100 points
Final exam will be worth 80 points
Mid-term exam will be worth 80 points
The homework will be worth 110 points
The quizzes will be worth 50 points
Class participation will be worth 30 points
At the end of the semester, the point totals from each
category will be added together and used to
determine the final grade
A
Grading Exams
A i 420 points There are 2 exams
B 2: 380 points - Mid-Term exam (80 points)
C £ 340 points D £ 300 points Scheduled during week 7 Final Exam (80 points) Scheduled during the final exam tune There is time allotted in class to review for both exams
The following point scale will be used to determine There are two exams for the course.
the final grade in the course The mid-term exam, worth 80 points, is scheduled
As will require greater than or equal to 420 points dunng week 7.
Bs will require greater than or equal to 380 points The final exam, worth 80 points, is scheduled dunng
Cs will require greater than or equal to 340 points the final exam time.
D's will require greater than or equal to 300 points There is time allotted in the syllabus for review for both exams
The exams will be made up of matenal that has been covered in quizzes, homework, and other unique questions that come up dunng the course of the semester.
Taking of the exams at a later date than scheduled is
not nermitted unless nnor arraipnments have been
6
8
20


Homework
Final Project
Worked on in groups of 3 or 4
Each group will be given a unique space
and budget and be asked to present an
appropriate acoustical solution.
- Solutions will be presented in class
- A write up will be prepared for the instructor
More information in the syllabus
Due by Final Exam Review
A final project will be worked on in groups of 3 or 4
students
Each group wilt be given and unique space and
budget and will be asked to present an appropriate
acoustical solution.
Each group will prepare a formal WTite up or their
solution to be handed in as well as be given IS
minutes to present their solution to the class
The final project is due the day of the final exam
review
For more detailed information, see the course
syllabus---------------------------------------------
Will be assigned at the beginning of a topic
Will be collected at the beginning of the
next topic
Changes to due dates will be announced in
class and made apparent on homework
handouts
No unexcused, late homework accepted
Homework will be assigned at the beginning of each
new topic and collected at the beginning of the next
topic
Changes to due dates will be announced in class and
made apparent on homework handouts.
No unexcused, late homework will be accepted
Students are encouraged to form study groups with
other students in the course to work on homework
Each student may work with other students on the
homework, but they will be expected to turn in their
homework individually Homework turned in as a
group will nnt he acrepted Although students can
work together on homework, they should make sure
to understand the homework material individually as
it nil) h on ill* miH.I*rm and final name
Quizzes
Unannounced so come prepared'
You must be present in class to take the
quiz unless prior arrangements have been
made
Class Participation
You will be graded on effort put into
- class discussions
- asking questions
- Paving attention to the instructor and student
presentations
- Not sleeping, talking on the phone, text
messaging, etc.
Quizzes will be given periodically throughout the
semester unannounced.
You must be present in class to take the quiz unless
prior arrangements have been made
The quizzes will cover material from the previous
lecture and assigned readings, so it is a good idea to
review new material after each class.
The quizzes will not be difficult and only take 10
minutes of class. They will, however, gauge whether
or not students have been paying attention and
reviewing outside of class.
u
Students will be graded on class participation.
Participation includes:
-asking questions about the homework
-Posing answers to questions asked in class
-Not sleeping
Participation in class discussions
Paying attention to the instructor and other students
giving presentations
21


Attendance
Attendance is not required but..
It is in your best interest to attend class!1
Large amount of material
Quizzes are unannounced
Class participation will be recorded
Questions on Homework will be covered
There is no grade given for attendance.
However, it is in your best interest to show up for
class.
Questions on homework will be answered
Quizzes are unannounced
-Class participation is graded (if you are not present,
you are not participating)
-A large and diverse amount of material will be
presented
Review course outline Mention university holidays,
classes cancelled for AES or other conventions, etc.
Explain again how homework will be assigned and
collected Explain how die chapter readings
correspond to topics covered in class.
Explain that students are required to take notes
during the class They can download the power point
presentations if they feel that they need them or want
them to take notes on.
14
The Course Website
The course website is
www.DanieIHicks.coni/acoustics
Site will have
- Syllabus
- PowerPoint Presentations
- Homework Assignments
- Q&A Board
- Links to supplemental readings and websites
There is a website for the course at
www.damelhicks.coin/acoustics
The website will contain:
Updated Syllabus
-Homework assignments
Power point presentations
-Frequently asked questions about the syllabus/course
and their answers to clear up confusions
Links to supplemental readings and websites
22


Homework #1
Introduction
In 1 page of typed writing, answer the following questions:
How far along are you in your degree?
- Do you have much of a math background?
Have you previously worked on any projects concerning recording
acoustics?
What are you expecting from this course?
Who or what type of music are you currently listening to?
Also, include a current headshot photo inserted in the document.
Formatting:
Times New Roman or Arial, 10 or 12 point Font, single space between sentences,
double space between paragraphs
(NOTE: This formatting will be expected on all future writing assignments)
Format Example
Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy
eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua.
At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no
sea takimata sanctus est Lorem ipsum dolor sit amet. Lorem ipsum dolor sit amet,
consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et
dolore magna aliquyam erat, sed diam voluptua.
Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy
eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua.
At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no
sea takimata sanctus est Lorem ipsum dolor sit amet. Lorem ipsum dolor sit amet,
consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et
dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo
dolores et ea rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem
ipsum dolor sit amet. Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed
diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed
diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita
kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet.
23


4.2 Math Review and Homework 2
This math review topic covers basic math requirements that will be necessary
for the student to master for success in the course. The subjects covered in this topic
include:
Concepts in basic algebra
Exponentials and Logarithms
Linear and Logarithmic graphs
Octaves
Scientific Notation
Introduction to sine waves
English and Metric unit systems
The decibel
24


Acoustic Fundamentals of Critical Listening and
Performance Spaces Topic 2 Review
Daniel Hicks
All pictures and images are creations of the author
unless otherwise specified.
What well cover
Algebra and Logarithms
Linear and Log Graphs
Define Octave
Scientific Notation
Sine Waves
Metric and English unit systems
Define "Decibel
We will cover:
-Algebra and logarithms
How to read linear and log graphs
-Define octave
-Talk about working with scientific notation
Describe the properties of simple sine waves
-Learn the difference between metric and english unit
systems
-And define the decibel
.-i-
Basic Algebra Basic Algebra
Algebra is math using variables * Variables can be manipulated just like numbers
Exiofk:
Area of a square is Length x Width Exu^r
A = LxW If A=2, B=3. C=7
m ^ + ^ Can be written as 7 C
Algebra is math using variables
For example, the area of a square is length times
width and can be written in short hand as L times W
In algebra, its important to remember that you can
manipulate variables just like you can manipulate
numbers.
Often, it is easier to write quantities as variables m
equations and then substitute the number values of
the variables in dunng the final phase of solving an
equation.
25


Basic Algebra
multiplication : A x B, A B, or AB
A
division : A + B, A B, or
exponentials: Ab, or tfA
logarithms :logs(>4)
B
There are different multiplication and division
symbols that you will see used throughout this
course
Exponentials and roots are straightforward.
There are different versions of logarithms that you
may see written differently. We'll cover those later.
Basic Algebra
Other operators
ii let* than: <
is greater than: >
it leu than or equal lo: £
is greater than or equal to: 2
is approximately:
approximately orcqual to: s
is not equal to *
is defined as:
There are some other operators you should know that
you may see used in the course.
m-.-.a.
Exponentials Logarithms
2" =16 2-2-2-2 = 16 A logarithm is the exponent to which the base is raised, to produce a given number
2* = 16 or n- 4 n is called the Exponent 2 is called the Base 24 = 16 4 is the exponent to which 2 must be raised to equal 16 4 is the logarithm of 16 with base 2
An exponential is a number that is used to signify how many times a "Base is multiplied times itself. A logarithm is another way to express the exponential equpation
In the example, 2 needs to be multiplied to itself 4 times to equal 16. Therefore, the exponential is 4. When you get confused, keep in mind Two words, same equation1
In the example 4 is the exponent that 2 needs to be raised to, to equal 16.
Talk about the same thing in a different manner. 4 is the logarithm of 16, with a base of 2.
7
26


* Mil iUmlMtu nil
Logarithms
In the Math universe, there are 2 common
Bases used in nearly all logarithm equations
-Base 10 wntten as just plain log
- Base e...also known as the natural log. la
* In the Music universe,
- Base 2 is also common
Wntten u log,
In the mathematics taiiverse, there are two common
bases that you will see: Base 10 and Base e, also
known as the natural log. Notice that Base 10 is
wntten log and Base e is wntten In. If there is no
subscnpt with the log, always assume base 10.
In the music universe, Base 2 is often used We'll
talk about Base 2 more when we get into octaves.
Linear vs Logarithmic Scales
On a linear scale, the change between any
two values is a constant, linear amount
On a log scale, the change between any two
values is a change in ratio
9
10
Linear vs Logarithmic
Linear may be more convenient for us to
think about but...
our heanng responds in a loganthnuc fashion
Its very important to note that the linear scale and
logarithmic scale are very different.
On a linear scale, the change between two values is
an additive amount.
On a log scale, the change between any two values is
a change in ratio. For Base 10, that ratio is 10:1. For
base 2, the ratio is 2:1. Etc
Logarithmic scales are used to express systems with a
very large dynamic range. Human heanng can hear
from 20 Hz to 20,000 Hz. If you have a limited space
to represent that large range, a logarithmic scale is
the mnst efficient twie tn use_____________________
The other reasons why we choose to use log scales in
acoustics so often is because our heanng responds in
a linear fashion. For example, most of use will be
able to determine the difference between a SO Hz
tone and a 60 Hz tone. No one, however, will be able
to determine the difference between 6000 Hz and
6010 Hz, however Our ears respond in a logarithmic
fashion, so the logarithmic scale is beneficial for us
to understand and use.
n
12
27


Scientific Notation
The Octave
A change in 1 octave is a doubling of
frequency
- 100Hz to 200Hz and 1000Hz to 2000Hz are
both a change in 1 octave
The octave is a logarithmic scale with base
2 (ie. logj)
Scientific notation is an easy way to rewrite
very large and very small numbers
64780000 6 478-10' d.im.i.uii.
0.00002-2-10- b
(6.478 I0)-(2 1 An octave is a doubling of frequency.
The octave scale is a logarithmic scale with a ratio of
2:1.
In the range of human hearing, we can hear about 10
octaves.
Scientific notation is an easy way to represent very
large and very small numbers.
For example, the threshold of hearing is 0.00002
Pascal's. It is much easier to write 2x 10*5 Pascal's
when working with a lot of numbers. This will make
it less likely that you will misplace a 0 or accidentally
move the decimal point
Sine Waves
Sound is often depicted as a sine wave
The equation for a general sine wave is
y Asin(at-4)
13
14
Sine Waves
y Aim{a>t-)
Amplitude is controlled by A
Frequency is controlled by - Frequency may also be represented by/
Phase shift is controlled by "phi"
t stands for time
We often see sound depicted as a sine wave,
therefore, its important to understand how sine
waves function and what they mean
A sine wave is a periodic function, meaning that it
repeats itself, and is made up of 4 components. The
most obvious one we will see most often being Time,
or the variable t Sine waves may also depend on
population, or fuel supply, etc. Well always be using
time.
The second most obvious variable is 'omega' or
sometimes 'lambda', which is the frequency of the
sound that we are describing Higher frequencies are
represented by sine waves that repeat quicker
Volume or Loudness is represented by the variable A,
whirh mnltinli#c with th* tin* fimrhnn A lrtid*r
The variable is omega' or sometimes lambda' or f,
which is the frequency of the sound that we are
describing. Higher frequencies are represented by
sine waves that repeat quicker.
Volume or Loudness is represented by the variable A,
which multiplies with the sine function. A louder
sound will have a larger value for A than a small
sound.
The vanable phi is the phase relationship of the
sound with respect to time. We'll see how that is
important in a little bit.
Sound waves alway s propagate with time 1______________
16
28


The upper left wave is represented by sin(x).
If we multiply sin(x) by an amplitude of 4, we get the
upper right wave.
The lower left wave is the same as the upper right
except that it is phase shifted a negative 30 degrees.
The lower right wave is the same as the upper right
except that it has 3 times the frequency.
Sound is always represented in sine waves, we'll see
why in the next topic.
An example of some of the common english and
metric units and conventions.
We will be using both unit systems throughout the
course.
English vs Metric Systems
It's very important to know which system
you are working with
- EiigliA and Metric units arc not compatible
- You must choose 1 system and use it
throughout!
- Specific formulas are derived in one specific
system and are not directly compatible with the
Unfortunately, (from an easy-mat hematics
perspective) the United States has not adopted strict
use of the metric system like most other countries.
Therefore, we will always see equations written for
english units and metric units. In most cases, these
english units will not work in equations designed for
metric units and vice versa. It is ALWAYS true that
english and metric units can not be mixed together in
an equation (unless h is an equation that is designed
custom).
If we are to calculate accurate information, we
always need to know which unit system we are
working in and what specific equation or formula is
necessary for our units.
17
Luckily, time is always measured in seconds!
18
The Decibel
Developed by Bell Labs as a way to
compare two values
p, is a pressure we measure io Pascals (Pa)
is 2*ia5 Pa (threshold of bearing)
The decibel was developed as a way to measure two
values. A measured value versus a reference value.
WeU discover exactly how this came into existence
in a later topic. When audio engineers talk about
decibels, however, they are mostly likely talking
about dB Sound Pressure Level. Its important to note
that the decibel is referring to the equation that is
used. There are other decibels such as dB Sound
Intensity Level which is very different than sound
pressure level. We'U cover this also in a later topic.
Its important to note that from now on dB
measurements are classified. For example, dB SPL
for sound pressure level or dB SIL for sound intensity
level, etc.
19
20
29


The Decibel










A table with typical dB SPL levels.
Its commonly thought that sound pressure levels
much greater than the threshold of pain are
impossible. They are not... but they will have no
problem rupturing your eardrum!
21
30


Homework #2
Math Review
(answers in italics)
1) Solve the following:
25 = 32
log2 32 = 5
log3 6561 = 8
35 = 243
In 6 = 1.79
log 4 = .602
, 4 logr -.097
log 4 log 5 = -.097
2) Indicate whether the scale is linear or logarithmic (circle one):
Linear') Log
2 4 6 8 10 12 14 16 18 20
Linear
dLog^
3 6 12 24 48 96 192 384 768 1536
31


Linear
1 1.3 1.7 2.2
3) Match the function with its graph:
A) y = sin(x)
B) y 5 sin(x)
C) y = sin(x-30)
D) j; = ^sinO)
E) y = sin(4x)
F) y 2sin(2x)
2.9 3.7 4.8 6.2 8.2 10.6
32


Amplitude
4) Convert the following to/from Scientific Notation:
4659000 = 4.659x106
8990.432 = 8.990432x10s
4.89045x108 = 0.0000000489045
53.789xl03 = 53789
33


5) Solve the decibel equation for the following values:
dB = 20 log f p, 1
10 )
Pi = 1 93.98 dB
87.95 dB
Pi = .5
Pi = 2 100 dB
Pi = 0.1 73.98 dB
34


4.3 Sound Waves and Homework 3
The sound waves topic covers basic concepts of wave mechanics. The
subjects covered in this topic include:
Definition of a Sound Wave
Transverse and Longitudinal waves
Sound as a pressure disturbance
The representation of sound as sine waves
Frequency, period, and wavelength
Constructive and destructive interference
Complex waves
Sound propagation and the speed of sound
35


What well cover
Sound and Waves Define Sound Wave Longitudinal and Transverse Waves Wave Mechanics - Frequency, Period, and Wavelength - Interference - Complex Waves Sound Wave Propagation The Speed of Sound
Acoustic Fundamentals of Critical Listening and This topic will cover:
Performance Spaces Topic 3 Sound and Waves -What we mean when we talk about Sound Waves
Daniel Hicks -The difference between Longitudinal and Transverse Waves
All pictures and images are creations of the author unless -How waves behave; Frequency, Period, Wavelength,
otherwise specified. Constructive and Destructive Interference, and Complex addition
How waves propagate -And the speed of sound and how its determined
J 1 1 1 I i i
Sound Waves Sound Waves
Sound Wave is a pressure disturbance that Pressure is a Force per f
travels through an elastic material. Wat Area p
- To some extort, all materia] is elastic and A
capable of transmitting sound ^(english units)
- We will be mosdy concerned with sotmd F
travdn g through air = Pa (Pascal in SI units) m
0.020855
,D.
Most sound that we talk about is created from a pressure
disturbance in the air that has a frequency that we can hear
(between 20 Hz and 20 kHz). Sound can also travel
through other media like water and solids. Sound cannot
travel through a vacuum because there is nothing in the
vacuum to carry the pressure disturbance.
When we talk about acoustics, we normally think about
sound that travels through the air. However, controlling
sound that travels through solids, called isolation
acoustics, is also a major branch of acoustics and is
normally the most expensive part of an acoustic design.
Well cover that in a later topic.
Animation courtesy of Dr. Dan Russell, Kettering
Univeisiiy-------------------------------------------------
Pressure is defined as a force per unit area.
Remember, proper units are necessary!
3
36


*
Transverse vs Longitudinal Transverse vs Longitudinal
* Thcreare two different types of waves Longitudinal (aka: Pressure Waves)
Transverse Waves that vibrate perpeadkmkr to their dkolion of - Waves that have their vibration along the direction of their propagation
WBBm
- Sotmd in air travels in Icngitudinal waves
- Ouittr and Piano nriagi vibrate ia a tnamcneawDer

There are three different types of waves: Transverse,
Longitudinal, and Water waves. Well mostly be
concerning ourselves with Longitudinal waves because
this is the way in which sound propagates through air.
Well touch briefly on Transverse waves in the Isolation
Acoustics topic when we explore how structures vibrate.
Something is said to be vibrating transversely when the
vibration is perpendicular (at a 90 degree angle) to the
direction of propagation.
Guitar and piano strings vibrate in a transverse manner.
Animation courtesy of Dr. Dan Russell, Kettering
University._____________________________________________
Longitudinal waves vibrate in the same direction as their
propagation.
This is the way sound vibrates in air.
Its important to note that the molecules that allow the
sound to propagate do not move in one direction. They do
vibrate side to side as the pressure increases and decreases,
but they do not move to create a wind.
Remember, sound is a pressure wave not an air wave.
Pressure moves through the air at a certain velocity. The
molecules of air do not have a net velocity.
Animation courtesy ot Dr. Dan Russell, Kettering
University.
Transverse vs Longitudinal
Both Transverse and Longitudinal waves
are typically represented by a sine wave
- For longitudinal waves the sine wave represents
the pressure distribution alooa the wave
Longitudinal Waves
Particles in a longitudinal wave oscillate
A Pressure Wave propagates
Air particles do not travel at the speed of
sound
- packets of ir pressure travel at the speed of
somd
So, why then, if sound waves are longitudinal, do we draw them as sine waves moving through the air? Some key things to remember when talking about Longitudinal Waves
-Its convenient -Particles of air oscillate (vibrate) back and forth as the pressure wave moves through them
-The sine wave actually shows us the pressure gradient, not the actual placement of air molecules in the air. -The pressure wave propagates (has a velocity) -Air particles do not propagate (have no net velocity) -The pressure waves travels at the speed of sound.
Well talk about the factors that determine the speed of sound in a little bit
Animation courtesy of Dr. Dan Russell, Kettering University.
7
8
37


Wave Characteristics
Frequency, f, is the measurement of
oscillations per second
- Given the unit Hertz (Hz)
I;
Wave Characteristics
A Poiod, T, is the uServal of time between
recurring oscillations
/ = - r
Frequency and period a
have a rccipricol relationship ! *" 7.85 Hz
r Eqh
/ .127 mc

Frequency is the measurement of oscillations, or The Period of a wave is the interval of time between
vibrations, per second. recurring oscillations.
One oscillation, or vibration, per secood is defined as 1 Frequency and period are reciprocals of eacbother.
Hertz (Hz) When frequency increases, period gets smaller.
Human hearing operates in the range of about 20 to 20,000 Hz.
9
10
,
Wave Characteristics Wave Interference
Wavelength, X, is the distance the wave will propagate in one period defend to the wave fteqatacy by the speed of mod, c There are two types of wave interactions - Constructive Interference - Destructive haerference
c lfc-1130 tbc.* 7.15 Hz ^ _ ware will aivel 144 feel evtxy f depending oe the pface icferioodiip of the waves
Wavelength is the distance a wave will propagate in one When two waves occupy the same space, they can interact
period in three ways. Constructive interference
Wavelength is related to frequency by the speed of sound. Destructive interference
-Something m between
As the frequency increases, wavelength decreases. As the period increases, wavelength increases. The phase relationship between the two waves determines which type of interference will occur.
n
12
38


Wave Interference
Wave Interference
* Constructive Interference
Destructive Interference
___________ __ When two waves we oat
, '''] of phase, they subtract
vA/\A

When waves are m phase, they will combine. When two waves are out of phase, they will also combine but it will act as subtraction.
This is called Constructive interference. This is called destructive interference.
Animation courtesy of Dr. Dan Russell, Kettering University. You can also think about this like adding 2 and -2 together. The effect will be cancellation.
Animation courtesy of Dr. Dan Russell, Kettering University.
13
An easy way to hear both types of interaction is with the phenomenon called 'beating'. Talking about simple sine waves is necessary when first thinking about sound, but real life sounds are actually very complicated.
When two waves are slightly different frequencies, the phase relationship of the two waves changes periodically. This sounds like the combined tone is beating. This example shows a fundamental and two harmonic sine waves.
Animation courtesy of Dr. Dan Russell, Kettering University.
is


Sound Wave Propagation Speed of Sound
Sound from a single ^ . * There are 2 variables that determine the
source propagates in j | speed of sound in air
a spherical shape in ^ , - Ten^jerattne
all directions - Humidity
The most important factor is Temperature
= (331.5 + (0.6 ,)) 344
c-,49 J459-4 + . .1130-
riMMin ifn DmBdlKfai^thinniy
fts also convenient to think about waves as traveling in Technically speaking, the speed that a wave propagates is
one direction from the source. In actuality, sound for a determined by the elasticity of the material it is moving
sound propagates in a sphere in all directions. through. For sound, it is more convenient to think about the speed of sound being determined by two variables.
Animation courtesy of Dr. Dan Russell, Kettering University. These are:
-Temperature -Humidity
The most important factor is temperature and humidity is usually ignored.
17
40


Homework #3
Sound and Waves
(answers in italics)
1) Describe the difference between Transverse and Longitudinal waves and give a
few examples
Transverse waves vibrate perpendicular to their direction of travel. Musical strings
like pianos, violins, and guitars vibrate transversely.
Longitudinal waves vibrate along their direction of travel. Sound waves vibrate
longitudinally.
2) a) Define Frequency and Period
b)What is their relationship?
Frequency is the measurement of oscillations per second.
Period is the time measurement of one complete oscillation.
Frequency = 1 / Period; they have a reciprocal relationship
3) a) Define Wavelength
b) How is wavelength related to the speed of sound and frequency?
c) What is the wavelength of a 30 Hz tone (c=l 130ft/s)
d) What is the wavelength of a 14kHz tone (c=l 130 ft/s)
Wavelength is the distance a wave will propagate before starting a new period
Wavelength = Speed of sound / Frequency
c) 37.66ft
d) .08 ft = .97 inch
4) Describe Beating. Why does it happen?
Beating is a type of wave interference that occurs when two tones are played that are
close, but not exact, in frequency.
41


Because the two tones are close in frequency, but not exact, a pattern of constructive
and destructive interference occurs where the two tones will amplify and then die out
together. This gives the perception of beats.
5) What is the speed of sound
a. In Denver at 70 degrees F
b. In Boston at 80 degrees F
The speed of sound is dependant most on air temperature. Humidity does play a role,
but is negligible.
c=(331.5 + (O.6.0c))*344-
s
s
a) 1127 ft/s
b) 1138 ft/s
42


4.4 Psychoacoustics and Homework 4
This topic covers basic psychoacoustic principles as they apply to the field of
acoustics. These topics may or may not have been introduced in other courses in the
program before this course. If they have been covered before, this will be a good
refresher and relate them to the study of acoustics. If they have not been covered
before this course, this will provide an adequate introduction. The subjects covered in
this topic include:
The range of human hearing
Perceived loudness
Equal loudness contours
Frequency and temporal masking
Sound source localization
I
43


Psychoacoustics
Acoustic Fundamentals of Critical Listening and This topic will cover:
Performance Spaces Topic 4 Psychoacoustics -The range of human hearing
Daniel Hicks -Equal Loudness Contours
-Frequency and Temporal Masking
All pictures and images are creations of the author -Localization due to Level, Time. HRTF. and
unless otherwise specified. Frequency cues
What well cover
' Range of Hearing
' Equal Loudness Contours
Masking
- Frequency Masking
- Temporal Masking
' Localization
- Level Time. HRTF, Frequency'
Range of Hearing
1 Theoretical frequency range of hearing is
about 20 Hz to 20 kHz
- Most adults cannot hear much below 40 Hz
1 Perceived loudness is frequency dependent
- Our ears arc most sensitive to frequencies
between 2 kHz and 5 kHz
- This frequency range is also where most speech
communication takes place
The theoretical frequency range of hearing is about
20 Hz to 20 kHz although most adults cannot hear
much below 40 Hz.
Loudness is a subjective quality. Amplitude can be
measured but the perceived loudness of that tone can
only be measured by asking listeners to desen be it.
These tests were first completed by H. Fletcher and
W A. Munson. It was found that loudness is
frequency dependant. Our ears are most sensitive to
frequencies between 2 kHz and 5 kHz. which is also
the frequency range where most speech
communication takes place
Equal Loudness Contours
First measured by H. Fletcher and W A.
Munson
' Defines a unit of perceived loudness called
Phons
A Phon is a measure gathered from listening
tests
- 1 Phon is equal to ldB at 1kHz
- All other values are subjective
In the measurements by Fletcher and Muson. a unit of
percieved loudness was developed for their
expenmenls called the Phon.
A phon ts measured from subjective listening tests
except for one point.
-1 phon is equal to 1 dB at 1 kHz
All other points are determined from listening tests.
44


Frequency Masking
Simply speaking:
Louder sounds will mask quieter sounds
- When played at the same time
- And their frequencies are close together
Pure tones will mask differently than noise
tones
These are the Equal Loudness Contours that
eventually developed from the tests by Fletcher and
Munson
You can see from these curves that all Phon levels
are not the same dB throughout all frequencies For
example, at 30 Hz, the 20 Phon curve is at about 75
dB SIL. At 1000 Hz the 20 Phon curve lies at 20 dB
SIL
All acoustics needs to be thought of as being
frequency dependent. These measurements highlight
just one instance that shows how different frequency
sounds behave in different ways.
Image from Wikipedia:
There are two types of masking that can occur that
will inhibit a listener from hearing sound even though
it is present.
The first, and most intuitive, type of masking is when
louder sound mask softer sounds. This happens when
the two sounds are played at the same time and their
frequencies are sufficiently close together.
Its important to note that this ty pe of masking
depends on:
The types of sounds present
Noise masks differently than pure tones
Louder sounds will mask better than quiet sounds
Wikipedia contributors (2006). Equal-loudness
Temporal Masking
A loud sound will mask quieter sounds that
occur immediately before (pre-masking)
and after (post-masking)
This graph shows the phenomenon of frequency
masking and some conditions that it occurs.
-Loud sounds will mask sounds of higher frequency
but not of lower frequency
-Soft sounds will not mask other soft sounds unless
they' are close in freuqnecv
Image courtesy of HyperPhysics:
Nave, C. R. (2006) HyperPhysics, retrieved May 7,
2006 from http://hyperphysics.phy-
astrgsu.edu/hbase/sound/mask.html
A less intuitive type of masking is temporal masking
A louder sound will mask quieter sounds that occur
-immediately after (post masking)
-Immediately before (pre masking)
No one really knows exactly how loud sounds will
mask quieter sounds that occur before the loud sound,
but it does happen
6
8
45


Localization
Localization of a source depends on three
effects:
- Time delay between both ears
- Level difference between both ears
- Head Related Transfer Function (HRTF) effects
! *
laaitcouisyorMidiaalV
The process in which a human can determine the
ongin of a sound is called localization.
Localization depends on 3 factors:
Time delay of sound between the two ears
Level difference of sound between the two ears
Head Related Transfer Functions that affect different
frequencies from interaction with the head
Image courtesy of Michael V Capps, Ph D :
Capps, M. V. Adding Sound to Virtual Reality
Retrieved May 9, 2006 from
http://www.es nps.navy.mil/people/faculty/capps/447
3/projects/OlSummer/soiaid/SoundSoftwareDepth.ht
"m
Localization Time and Level
In General...
Sounds
Arriving up to 40 ms after the direct sound
Are less than iOdB louder
are perceived as coming from the same source
Sounds
arriving 40 ms or more after the direct sound
are heard as separate sounds
This effect is called the Haas Effect Precedence
Effect or law of the first wavefront
In general, sounds arriving up to 40 milli-seconds
after the direct sound and are less than 10 dB louder
than the direct sound are perceived as coming from
the same source
Sounds arriving 40 ms or more after the direct sound
or are more than 10 dB louder than the direct sound
are perceived as coming from a difference source (an
echo).
This is called the Haas Effect Precedence Effect or
Law' of the First Wavefront*
9
Localization HRTF
For low frequencies, the wavelength size is
much greater than the head
- Sound wraps around the head, unimpeded
For higher frequencies, the wavelength size
is much smalls' than the head
- The head is seen as a bamcr to sound
These effects are called Head Related
Transfer Functions
Localization HRTF
The head effects different frequencies m
different ways
- Level differences between the ears at low
frequencies are small because low frequencies
easily wrap around the head
- Level differences between the ears at mid-high
frequencies are large because the head creates
an acoustic shadow-
10
As with all subjects in acoustics, localization is
frequency dependent
The wavelengths of lower frequencies are much
larger than the size of a human head so sound easily
wraps around the head, unimpeded Higher
frequencies have shorter wavelengths that see the
head as a barrier These two effects describe the basic
concept ofHead Related Transfer Functions.
Because low frequencies can easily wTap around the
head, level differences at low frequencies between
the ears are very small. For the opposite reason, high
frequencies see the head as a barrier and there is a
large level difference between the ears
it
12
46


' *11 *
Localization HRTF Localization HRTF
Low frequency localization relies on time difference - Time difference between the two ears is used to triangulate" to find the source Mid/High frequency localization relies on level difference - Sound is perceived as coining from the direction of the louder level (within 40 ms Hus Effect cntcra) What happens if the sound is directly in front, behind, or above the head? - Time difference and Level difference are equal The pinna (outside parts of the ear) create different reflections into the ear canal affecting frequency response - Specific frequency responses are associated with specific directions
Because of these phenomena, low frequency
localization depends on the time difference between
the ears This time difference is used to triangulate
the position of the source.
Mid and High frequency localization takes advantage
of the acoustic shadow caused by the head and uses
level differences between the ears to determine the
direction of the source.
Even more complicated schemes are used to
determine the position of sound above, behind, and
directly in front of the head.
The physical design of the ear reflects different
frequency sounds into the ear in different ways. The
brain can interpret these slight differences due to
different positions to find the direction of the source.
13
14
47


Homework #4
Psychoacoustics
(answers in italics)
1) A 50 Hz tone and a 4 kHz tone are played at 60 dB.
a) Are they perceived to have the same loudness?
b) Why or why not?
a) They are not perceived to have the same loudness.
b) Different frequencies are perceived to be louder or quieter even if they are played
at the same SPL. This effect is documented in the Equal Loudness Contour plot.
2) Describe the two types of masking that can occur
Frequency masking: Where loud tones will mask quieter tones if they are close in
frequency
Temporal masking: Loud sudden events will mask other sounds that occur after and
slightly before
3) Without using their eyes, how do people know which direction a sound is coming
from?
Localization occurs from: Time difference between the ears, Level difference between
the ears, and Head Related Transfer Functions that happen around the head.
48


4.5 Acoustic Measurements and Homework 5
This topic is the first that builds significantly off of the previous topics and
gives information to the student that they probably have not seen before unless they
have previous experience in acoustics. The subjects covered in this topic include:
The definition of the decibel
Decibel addition
The inverse square law
SPL measurements and A and C weighting networks
Octave bands
Pink and white noise
Time and frequency domain representations of sound
The fast fourier transform
Impulse response
Early reflections and reverberation
Reverberation time
Measurement tools
Equipment calibration
Simulation tools
49


Acoustic Measurements
Acoustic Fundamentals of Critical Listening and
Performance Spaces Topic 5 Acoustic
Measurements
Darnel Hicks
All pictures and images are creations of the author
unless otherwise specified
This topic will cover
-Power and Pressure dB. the inverse square law, and
adding dB
Weighting curves used in SPL measurements and
octave bands
-The use of Pink vs White noise in acoustic
measurements
Time and the transformation to the frequency
domain
What well cover
The dB Revisited
2
Impulse Response
- Early Reflections
Reverberation Time
- Sabine Equation
- Eyring Equation
Measurement Tools
- Calibration
Simulation Tools
The use of the impulse response
The use of the sabine and erying equations to
calculate reverberation time
Tools used for measurements and how to calibrate
them
Auralizaoon and simulation tools
We've previously seen that the dB is.
But where did that come from?
We know the equation to calculate dB SPL but it
didn't just arrive to us
There are a few steps of derivauon to arrive at the dB
SPL equation that are helpful to understand.
3
50


The dB Revisited
The Bel. originally called a Transmission
Unit (TV), was developed to quantify the
reduction of sound Power over l mile of
telephone cable
BelPo*,r = lg~-
rtf
The dB Revisited
' It was later found that the Bel was too large
for every day use. so the decibel. 1 Bel.
was developed
I dB
Bel,
£2at- = logL
10
it/arow = lo-iog-
The Bel was developed to describe the reduction of
sound power of 1 mile of telephone cable
This was a useful measurement for Bell Labs during
the time they were stringing telephone cables across
the country.
After using the Bel in real world measurements, it
was found that it was still too large of a' unit to work
with
The decibel was developed. A decibel is one-tenth of
a Bel.
5
6
The dB Revisited
The dB Revisited
In acousUcs. we more interested in sound
Pressure, not sound Power
Pot p2
so
dBsrl = lOlog-^-r
P
In acoustic measurements, we are most interested in
sound pressure not sound power.
Power is proportional to pressure squared.
Simplify ing the logarithm expression
oB^lOlog-2^
P-r
becomes
dBgpL = 20 log -2i-
Prtf
When both the numerator and denominator is raised
to the same exponent in the logarithm, the exponent
can be multiplied outside of the logarithm
Thus, we arrive at the dB equation we are used to
seeing.
51


Adding Decibels
The dB is a logarithmic number, you cannot
simply add dB values together for multiple
sources
Adding 2 sources, each at 60 dB does not
equal 120 dB!
Logarithms, because they are exponential functions,
cannot be added linearly
For example, two sources, each at 60 dB, will not add
to 120 dB (the threshold of pain). If this were the
case, we would all be deaf if two people whispered at
the same time!
Atmam rfliirtu liMnnmiiM*- amm Ha
Adding Decibels
For adding n correlated sound sources at the
same level, use the equation..
dB9Um = dBJJUlu + 20 log n
where n is the number of sources
There are some useful equations that can be used for
specific instances when you need to add dB readings.
This equation can be used to add a number of
correlated sound sources that are all playing at the
same level.
9
Adding Decibels
Adding Decibels
10
The front 3 speakers of a 5 1 setup are
playing a pure tone (in phue and correlated) each
at 70dB, measured from the listening
position.
- What is the total dB at the listening position?
dBrim = + 20' log n
dB,^ = 70 + 20 log3 = 70+9.5
dBVLt =79.5 dB
Example of using the previous equation.
To add n correlated sound sources with
different levels, use the equation...
dBaL_ 20-log(anblog-f!- + nt,log-fi+ ,+antilog^L)
To add a number of correlated sources that are at
different levels, the equation become a little more
tricky
This equation converts each dB reading into it's
pressure (the antilog part of the equation), adds the
pressures, and then converts back to dB.
11
12
52


r*
Adding Decibels Inverse Square Law
Earanga PrcMn
The front 3 speakers of a 5 .1 setup are Sound radiating from a speaker can be
playing a pure tone (in phase and conelited) approximated as sound radiating from a
- #1- 50dB. #2= 70 dB. #3= 40 dB - What is the total dB? point source
<. 20 log(antilof-f^+analog ...+analog i.) The inverse square law states:
-20Iog00+10+l0")20-lot00=+105 + 105) - The intensity of the sound varies with the square of the distance
Sound that radiates from a source can be
approximated as radiating from a point source if you
are a sufficient distance from the source (in the far
field).
Because of this, the intensity of sound vanes with the
square of the distance from the source.
Inverse Square Law
tmegeceizwy ofC R. Nm ftt Hyprfltyuo
Sound from a point source radiates in a sphere.
If you double the distance, the area of that sphere
increases by four (the square). If you tnple the
distance, the area increases by nine (again, the
square).
This ratio in intensity corresponds to 6 dB SPL
Image courtesy of HyperPhvsics:
Nave, C. R. (2006) HyperPhysics, retneved May 7,
2006 from http://hyperphysics.phy-
astr.gsu.edu/HBASE/forces/isq.html
13
14
Inverse Square Law
For every doubling of distance, the dBspl will
decrease by 6dB
Therefore, for every doubling of distance, the dB SPL
drops by 6 dB.
This is what is commonly known as the inverse
square law
is
16
53


SPL Measurements
There are 3 main types of SPL
measurements
- Linear (dBllB)
- A weighted (dBA)
- C weighted (dBr)
Linear is performed by using the standard
dB equation _
dB-. =20-log-fi-
There are 3 main types of SPL measurements used
today
Linear (dB lin)
A weighted (dBA)
-C weighted (dBC)
Linear is calculated using the standard dB SPL
equation
SPL Weighting Curves
A and C weighting are based on the Equal
Loudness Contours
A-Weighting was developed for the
measurement of low level sounds (<- C-Weighting was developed for louder
sounds
A and C weighted were developed using the equal
loudness contours.
A weighted was developed for the measurement of
low level sounds. Because we hear mid range
frequencies better than low and high frequencies at
quiet levels, the low and high frequencies aren't
counted as much as the mid frequencies in this
reading. This gives a more accurate reading of
perceived dB SPL.
The C weighting was developed for louder sounds
Low frequencies are percieved only slightly softer
than mid and high frequencies at louder levels, so
they count in the reading just slightly less

SPL - Weighting Curves Octaves
\\ <7^ We've previously seen that the octave scale is a logarithmic scale with base 2 (te. log2)
/ For every octave, there is a doubling of frequency
s m.K< 2a ri iiiiiii

ofWikjmla iMo
Comparison of A. B, C, and D weighting scales. Weve previously saw that the octave scale is a log scale with a base of 2.
D was developed for aircraft measurements at airports B is rarely used This means that for every octave, there is a doubling of frequency.
Image coutesy of Wikipedia. Wikipedia contributors (2006). A-weighting Wikipedia, The Free Encyclopedia. Retrieved 19:48, May 9, 2006 from htip.//cn.wikipcdia.orE/w/mdCT.phD?tnle=A- weiehtine&oldid51375770
19
54


Octave Bands
The audio spectrum is often broken down
into smaller 'octave bands' for easier
analysis
Our ears respond to octave band
measurements better than frequency by
frequency analysis !
We use Octave bands for two reasons.
-ease of use
-Our ears respond in a logarithmic, octave fashion
much better than a linear frequency manner.
Octave Bands
* The typical 10 octave bands used are
31.5Hz 63Hz 125Hz 250Hz 500Hz
31 31 3) 51
1kHz. 2kHz. 4kHz, 8kHz and 16kHz
There are 10 octave bands that are commonly used
Sometimes, only the middle 8 or middle 4 are used
when precision isnt necessary.
21
22
Pink vs White Noise
It is common to use a broadband noise
source for measurements
There are two types of noise that are
commonly used for different tests
- Pink Noise
- White Noise
Instead of a sine sweep of frequencies from 20 Hz to
20 kHz, a broadband noise source is often used for
measurements over the frequency spectrum.
These sources are pink and white noise
23
24
55


Pink Noise s
1 Equal energy in all octave bands
3dB rolloff in narrow band
S1) e II 1IU H a
Pink noise is defined as having equal energy in all
octave bands.
When looked at on an octave band scale, because
each octave band has equal energy, the octave bands
should all read the same dB SPL
When looked at on a narrow band or frequency by
frequency scale, you should see a 3dB rolloff. This is
because as you move higher in the octave bands, the
energy' is spread out over a larger and larger number
of individual frequencies (remember that each higher
octave band contains twice the number of frequencies
than the previous band) This causes a rolloff.
Because Pink Noise is equal energy for every octave
band, and octave bands nicely mimic the way our
ore h*ar Pint* ic mit new) in apnixtir
White noise is defined as equal energy at each
frequency
On a narrow band scale, equal energy per frequency
shows up as a straight line.
On an octave band scale, white noise shows up as a 3
dB increase for every increasing band because there
are more individual frequencies in higher octave
bands than there are low bands
Most often, measurement systems are provided with
white noise sources, because it is easier to create, and
then a filter is applied to create Pink Noise
Time vs Frequency Domain
> So far, we've been changing between time
and frequency information without much
notice.
^-U
But it is easy to get confused!
Time vs Frequency Domain
An acoustical even is described by 3 items
Energy or Amplitude (dB)
- A time thtf it takes place
Specific fttquf ty where it takes place
So far, we've been talking about measuring an acoustic event that happens in the time domain (happens over some amount of time) and then converting that information into octave band graphs, which are in the frequency domain (happen over different frequencies). An acoustical event needs 3 bits of information in order to be described completely -energy or amplitude (needs to be big enough to measure) -A time that it takes place -A specific frequency that it takes place
It's easy to talk about this, but the actual process is a little more difficult to understand. Without all 3 of these parts of information, we cannot intelligently talk about an acoustic event.
27
56


i n !
Fast Fourier Transform (FFT) Impulse Response
We make use of a specific Fourier The impulse response of a system is it's time
Transform, called the FFT. to convert domain response when presented with an impulse
between time and frequency information signal The impulse response is a signature" of the room
During the conversion process, no information is lost Amplitude. Frequency and Time information is - Contauis ail info to describe an acoustic event m Time and Frequency domains - The FFT is used to convert the Impulse Response into frequency infomtaaon
always available
To convert from time based information to frequency
based information, we use a special type of fourier
transform called the fast fourier transform, or FFT
After this conversion takes place and we have
frequency information, we can then convert back to
the time domain and get the same information we
started with. Its important to realize that we don't
lose information during the conversion, we only
convert it
You can think about the process in terms of currency.
If we want to buy Canadian goods, we convert our
money into Canadian money to use it If we choose to
convert it back at any time, we can
The acoustic measurement called the Impulse
Response is a time domain response of a system
when presented with a test signal
It is often described as the acoustic signature of a
room.
Sound from a source is measured m the room.
The various reflections in the room will present
information that is unique to that specific room.
Typical impulse response graph
31
32
57


Impulse Response
The impulse response will show
- Early reflections
- Reverberation and Reverberation Time
- Energy level of reflections
- Can be converted into the frequency domain
The impulse response will show
-early reflections
-Reverberation and reverberation time
-The energy level of reflections
Again, this information can be converted into the
frequency domain to talk about specific frequencies.
Specific frequencies will react differently in the
room.
Early Reflections
Early reflections are useful when
- Localizing sound
- Trying to create "spaciousness
- Broadening an image
Early reflections are harmful
- When they are too loud, they will cause
'muddiness''
- Can create comb filtering
Early reflections are useful when
-trying to localize a sound
-Trying to create a sense of 'spaciousness (is the
room large or small?)
broadening' an image (making a thin snap into a
large crack)
They are harmful what
-they make sounds 'muddy' when they are too loud
-They create comb filtering
33

Reverberation occurs when room reflections become
so closely spaced that they can no larger be
differentiated as individual reflections
This happens after 40 ms of time has passed unless
the reflection is very loud
Reverberation Time RT60
Defined as the length of time it takes for a
60dB decay after a sound source stops
- Time varies with the dimensions of the room
- Vanes with loom contents
Reverberation time is defined as the length of time it
takes for a 60 dB decay in reverberation.
Reverberation time vanes with the size of the room
and with the amount of absorption present in the
room.
34
35
36
58


RT can be calculated using the Sabine Formula
AMWUt feaMnmk
Reverberation Time RT60
1 If the absorption in the room is not
uniformly distributed
Or
One dimension of the room vanes greatly
(one dimension is much longer than the
others)
The Eynng Equation should be used instead
The Sabine equation is an approximation of a more
complex equation that assumes
absorption is uniformly distributed throughout the
room
All dimensions of the room are relatively the same
size
tf these assumptions are not correct, the eyring
equation should be used instead
37
Reverberation Time RT60
Reverberation Time
Eyring Equation
0.049-V T 0.161 ^
-Sln(l-o) -Sln(l-a)
The best RTW for a space depends on
- Size of the space
- Use of the space
- T>pe of music, or speech, or both
Slow and solemn=Long RTM
Quick and Rhvthmic=Short RT^
38
The eynng equation.
The appropnate RT for a space depends on
-the size of the space
-The use of the space
-The type of music or speech performed in the space
For example, slow and solemn music would benefit
from a long reverberation time. Quick and rhythmic
music wouldn't be intelligible.
Quick and rhythmic drum solos would benefit from a
short reverb time Slow, solemn gregonan chant
would sound thin and dry.
59


Reverberation Time
Reverberation Time, just like all other
acoustical events, is Frequency Dependent!!
- Higher frequencies will decay different than
lower frequencies depending on the types of
Measurement Tools
There are many different types of
measurement tools
- Varying price ranges
- Varying ease of use
- Varying measurement capabilities
ke= 7W.~' cat!
Reverberation time, just like all acoustic events, is
frequency' dependent!
You will find that different frequencies take different
amounts of time to die out in a room depending on
the shape, size, and absorption in the room.
There are many different types of measurement tools
available to make acoustical measurements
With the increased availability of portable, pow erful
computers, the price of these tools continues to drop.
41
Measurement Tools
Handheld Sound Level Meters
Handheld sound level meters are the most basic of
measurement tools.
Most provide
-amplitude information in octave and 1/3 octave with
weighting curve settings
-More expensive models can calculate reverberation
time
And some have connectivity with computers for
further acoustic analysis.
42
43
44
60


Measurement Calibration
Before a measurement can be taken, the
system needs to be calibrated
- Microphone is given a specific frequency at a
SPL level with a pistophone j
- Software is also input with the calibration info
Both the microphone and software are given
the same calibration information
Acoustic Simulation
More complex modeling software will
allow simulation of any space
- High reliance on new computer technologies
Simulation software is still expensive
>S5000 in most instances
Programs will calculate most acoustical
parameters as well as provide Aurahzation
Before anv acoustic measurement, simple or More complex auralization software will allow the
complex, the measurement system always needs to be acoustic simulation of anv space with the use of a
calibrated! computer model.
Without a calibrated system, a measurement is Simulation software is still very expensive but is
useless. starting to drop in price as systems are refined and computer become more powerful.
The most common way of calibrating a measurement system is by
-feeding a measurement microphone a known level
-Imputing a correction factor into the system so that the output reading is the same as the known input level
45
46
61


Homework #5
Acoustic Measurements
(answers in italics)
1) Start with the definition of a Bel,
p
BelPower =logL
1 ref
and describe the steps necessary to come up with the definition of
d^spL = 20 log
Pref
1 dB=Belpower =logA
10 *pref
Pocp2
so
10-log-5-
V
=10-log-^4
Pref
dBSPL= 20-log A
Pref
2) The 4 front speakers in your car are each individually play at 70 dB SPL. What is
the measured SPL if they played all at the same time? (assume correlated and in
phase)
dBSPL, = ^sources
dB= 82 dB
62


3) The 5 speakers of your home theater 5.1 setup are measured the following
Left: 70 dB
Center: 75 dB
Right: 70 dB
Left Surround: 50 dB
Right Surround: 50 dB
If they are all playing the same thing (in phase and correlated) what is their
combined SPL?
dBcpr = 20 -log( antilog + antilog + ... + antilog)
SPL" 5 20 20 20
dB = 82 dB
4) At 4 feet away from a speaker, you measure 86 dB SPL. What is the SPL
measurement at 16 feet?
74 dB
5) A outside loudspeaker 8 feet away is playing at 110 dB SPL. How far away do you
have to be to measure 80 dB SPL?
256ft
6) How do the Linear, A, and C weighting curves for dB measurements differ?
Linear counts each frequency the same
A weighted is rolled off drastically at the low end and slightly at the high end
C weighted is rolled off slightly at the low and high end
A and C were developed with Equal Loudness Contour information
7) What are the two test signals used is acoustical measurements and how do they
differ?
Pink Noise: Equal energy in every octave band
White Noise: Equal energy at each frequency
63


8) a) What procedure do computers used to move from the time domain
representation of a sound to its frequency content?
b) If a waveform is transformed into frequency information, can it be transformed
back into a waveform?
a) Fast Fourier Transform or FFT
b) Yes, no information is lost during the conversion process. Use the inverse FFT
9) What is an impulse response and what information does it provide?
An impulse response is a time domain representation of the reflections in a room or
the room signature. It shows reflections, the energy of the reflections, and the
reverberation time.
10) What is the difference between a reflection and reverberation?
A reflection can be heard as a discrete event. Reverberation happens when the
reflections get so tightly spaced that they can no longer be heard as individual events.
11) What is reverberation time and how is it calculated?
Reverberation time is the time it takes for the sound to decay 60 dB in a room. It can
be calculated from the impulse response measurement.
12) A 1 kHz tone is played in a room and the reverberation time is found to be .45
seconds. If a 80 Hz tone was played in the same room, would the reverberation time
also be .45 seconds? Why or why not?
The RT may or may not also be .45 seconds at 80 Hz. A new test would need to be
run. Acoustical measurements are always frequency dependant!
64


4.6 Isolation Acoustics and Homework 6
This topic presents the concept of isolation acoustics and its use in acoustic
design. It is stressed that isolation acoustics are as important as interior acoustics,
although they may not be as interesting to look at. The subjects covered in this topic
include:
Site selection with regards to environmental noise
Describing noise
o NC, PNC, and NR rating systems
Transmission Loss
Sound Transmission Class
How to create STC measurements
The Mass Law
Coincidence and the effect of coincidence dip on STC
Structure borne noise
Room within room construction
o Multi-layer walls
o Floor construction systems
o Ceiling construction systems
o Doors and windows
HVAC considerations
The use of soundlocks
65


Isolation
What well cover
Site Selection
Describing Noise
-NC
-PNC
-NR
- Measurement Procedures
Transmission Loss
Acoustic Fundamentals of Critical Listening and This topic will cover
Performance Spaces Topic 6 Isolation Acoustics -Site selection with regards to isolation acoustics
Daniel Hicks -How to measure noise and describe it using the NC, PNC. and NR systems
All pictures and images are creations of the author unless otherwise specified. -Transmission Loss through a barrier
What well cover
Sound Transmission Gass (STC)
Mass Law
Acoustic Isolation
- Airborne Noi*e
Tnuiimitted Airborne Noise
Structure Borne Noise
Mass and Decoupling
Room within Room Design

What well cover
1 Isolation Solutions
- Walls
- Floors
- Ceilings
- Doors
- Windows
HVAC
1 Soundlocks
Sound transmission class of materials
Acoustic Isolation from airborne noise
Acoustic Isolation from structure borne noise
-The use of mass and decoupling to create isolation
-Typical isolation solutions
-HVAC considerations
-The use, and importance, of soundlocks
66


* **ll
Site Selection Describing Noise
* What is the easiest way to ensure a quiet An effective wav to describe an acoustic
studio? environment is by the level of ambient background noise
Build the studio at a quiet location! There are a few standards that rate ambient
If a quiet site is not an option, there is isolation acoustics Good, effective isolation is not cheap! background noise and produce a single 1 number rating

The easiest way to ensure a quiet studio is to build it An effective wav to describe an acoustic environment
at a quiet location is by the level of ambient background noise
If a quiet site is not an option, isolation acoustics can There are a few different standards that rate ambient
be used, but it is not cheap background noise to produce a single number rating
Effective isolation acoustics often costs more than intenor acoustics.
Noise Criterion
Noise Cntenon Curves (NC) are octave
band curves with a single number attached
to them
They were developed by Leo L. Beranek in
1957 and are still in wide use today
Many noise specifications today cite
specific NC ratings
Noise Criterion (NC) curves are octave band curves
with a single number rating attached to them.
There were developed by Leo Beranek in 1957 and
are still in wide use today in code and design
specifications

Noise Criterion

Above are the NC curves that describe the NC rating
system
6
67


To measure the NC of a space, octave band
measurements of the ambient noise of a space are
made and plotted against the NC curves
The rating of a space is the highest NC curve that
encompasses the octave band measurement.
Noise Criterion
Suggested NC Ratings________
Location Suggested NC
Recording Studio 15-20
Apartments 25-35
Counrooms 30-40
Classrooms 25-35
Restaurants 40-45
Movie Theatres 20-35
Here are some typical NC ratings.
Noise Criterion
9
10
Preferred Noise Criteria
Problems with the NC ratings are
- Large variation allowed at low frequencies for
good' NC ratings
- Only accounts for half of ihe audible spectrum
Still a very common rating used in industry
Some problems with the NC system include
-Large variability at low frequencies still allow for
good NC ratings
-Only accounts for half of the audible spectrum
The NC system is still a common rating used in the
design industry, despite these problems
The PNC is stricter at lower frequencies and
extends down one octave to 31.5 Hz
Suggested PNC Ratings
The Preferred Noise Criteria (PNC) is similar to the
NC rating system except that
it has stricter requirements at low frequencies
extends down one octave to 31.5 Hz
li
12
68


13
Noise Rating Curves
NR Curves are commonly used throughout
Europe
Suggested NR Ratings
Noise Rating Curves
NR Curves
14
Another rating system, found mostly in Europe, is the
Noise Rating (NR) system.
The suggested NR ratings are comparable to both the
NC and PNC ratings.
The NR system
is
16
69


Noise Measurement
To make an accurate measurement,
Calibration is absolutely necessary
Without a calibrated system, a measurement
is meaningless
Most calibration procedures call for
- Giving the microphone a known SPL using a
calibrator
- Correcting the reading to read exactly the SPL
input
An accurate noise measurement requires calibration.
A measurement made without first calibrating the
system is meaningless.
The most common way to calibrate a measurement
system is to
-give the microphone a known SPL level using a
calibrator
-Correcting the reading to match exactly the SPL
input given by the calibrator
K UMU d
Measurement Process
Diagram of the basic measurement process
17
18
Transmission Loss
Transmission Loss (TL) is the reduction of
sound from the passage through a barrier
S dBMdB-SSdB
Transmission loss is the reduction of sound level due
to the passage through a bamer
It is calculated by producing a broadband noise in
one room at a known SPL level and reading the
reduction in the second room, on the other side of the
bamer The reduction is the transmission loss of the
barrier
Because low frequencies behave differently than high
frequencies. Transmission Loss (like all acoustical
measurements) is frequency dependant.
Transmission Loss
* The equation to calculate TL is
n = £,-L,+101og-
A
where
L, the S PL Source Room
L, u the SPLm Rcmever Room
S u foul lurface area of the Banter
A is the total absorption of Reciever Room in Sabines (Sab)
(A is also known aTS'a)
The equation to calculate transmission loss is
straightforward.
The absorption of the receiver room can add to the
Transmission Loss but only a relatively small
amount, typically up to 2 or 3 dB SPL
19
20
70


Transmission Loss
Example
| SPLtS I kHz: 35dB
|V\4^I000S*

71>£,-£,!0lag- R.:tO-31*IOIac 71*:
A transmission loss calculation example.
Acoustic Isolation
A materials acoustical properties are
characterized by
- Acoustical Impedance
(frequency dependent tound resistance of e me ten el J
- Sound Propagation
(speed of sound through materiel)
All matenals are acoustical: They all
have an Acoustical Impedance and a
Propagation Constant!" -idnsuryk
A matenals acoustical properties are charactenzed by
its
the sound resistance of the material called acoustical
impedance (frequency dependent!)
-The speed that sound travels through the material
All matenals are acoustical and anything can be used
in an acoustical space. However, some matenals are
more economical and efficient.
21
Sound Transmission Class
WB By r ImI|
Sound Transmission Class
22
The Sound Transmission Class (STC) is a
TL vs Frequency relationship represented
by a single number
Generally speaking, the higher the mass of a
barrier, the higher the STC Rating
- This is known as the Mass Law"
The STC Curve consists of 3 straight lines
wi he ifl ere nt lq 2£& FU

at CUV r-

s L_
125 200 320 500 S00 1250 2000 3200
160 250 400 630 1000 1600 2500 4000
Frepency (Hz)
Sound transmission class relates transmission loss to
a materials frequency dependent nature and
represents it by a single number.
In general, the higher the mass of a bamer. the higher
the STC rating of the barrier and the better the barrier
performs at blocking sound. This is known as the
'mass law'
The STC curve consists of 3 straight lines with
different slopes
-3 dB per 1/3 Octave from 125 to 400 Hz
-1 dB per 1/3 octave from 400 to 1250 Hz
A flat line from 1250 to 4000 Hz
23
24
71


Sound Transmission Class
To use the STC Curve:
- A 1/3 Octave band reading is fitted to the STC
curve so that
No single difference exceeds 8 dB
Sum of differences is no greeter than 32 dB
The STC Rating is then given by the curves
position at 500 Hz
To use the STC curve, a 1/3 octave band
measurement of the transmission loss of a barrier is
made and fined on the STC curve. The STC curve is
'slid' up the graph until either
-A difference between the STC curve and the TL
measurement reaches 8 dB
The sum of the differences at each 1/3 octave
reading reaches 32 dB
The STC rating is then given as the curves position at
500 Hz
25
26
Sound Transmission Class
Frequnacy(Hz)
Sound Transmission Class
Ejf ile
_
: 2
: M ff. tb Im
: I ur
y s IB
123 200 320 300 800 1230 2000 3200
160 250 400 630 1000 1600 2300 4000
Frequency (Hr)
STC calculation example
The STC curve is fined to the measurement on the
graph
STC calculation example
The STC curve is slid up until the maximum different
between the curve and the measurement reaches 8 dB
27
28
72


STC measurement example
Or the sum of the differences between the curve and
the measurement reaches 32 dB.
The STC rating is then given by the curves position
at 500 Hz
Common STC ratings of typical construed on
materials
29
A * A
Sound Transmission Class Isolation Airborne Noise
For multilayer svstems. use the equation * 'Leaks' or gaps can have a devastating
axr, me, me. effect on airborne noise isolation
STC* I0-log(£l0 w *10 + ...+ 10 ) - Around edges of doors - Between window frames and walls
This value assumes perfect construction! Electrical
HVAC
* Cable troughs
The calculation of multilayer svstems like multiple walls is a bit more complicated Leaks or gaps can have a devastating effect on isolation
This equation assumes perfect construction! These problems most often occur around the edges of doors -Between window frames and walls
-Through holes cut in the walls for electrical wires, HVAC vents, and cable troughs
31
so
32
73


Isolation Airborne Noise
At best, the TL for a Leaky door is 7-12 dB
worse than a property gasketed door
I
A leak or hole in a bamer as little as 0.1% of the I
area of the boundary will bnng an STC of 60 I
down to an STC of 30 j
!
Small leaks can. and will, cause huge problems! I
Isolation Transmitted Noise
When sound energy hits a bamer
- Some will be reflected
- Some will be absorbed
- The rest will be transmitted through the barrier
The Mass Law states that for every
doubling of mass, TL will increase by 6dB
- Applies strictly to limp, non-ngid bamers
At best, the TL for a leaky door is 7-12 dB worse than a properly gasketed door When sound hits a bamer, some sound will be reflected, some will be absorbed, and the rest will be transmitted through the bamer
A hole as small as 0 1% of the area of the boundary has the potential to bring the STC of a bamer from 60 down to 30. For every doubling of mass, transmission loss of a bamer will increase by 6 dB
Small leaks cause huge problems!
33
34
Isolation Transmitted Noise
Most matenals used as bamers are rigid
- Because of this. TL is effected by
"reonnce" at low frequencies (<150 Hz)
'coincidence' at higher frequencies (>1500 Hz)
The coincident frequency greatly effects the
STC rating of barriers
The transmission loss of rigid bamers is effected by
resonance at low frequencies (<150 Hz) and
coincidence at higher frequencies (> 1500 Hz).
The coincident frequency greatly effects the STC
ratings of bamers.
Isolation Coincidence
The critical frequency' is the frequency at
which the wavelength of sound matches the
same wavelength of the bending modes of
the bamer
Every frequency of sound above the critical
frequency, at the correct angel of incidence,
will match a bending mode of the bamer
This is called Coincidence
The critical frequency is the frequency at which the
wavelength of sound matches the same wavelength of
the bending modes of the bamer.
Every frequency of sound above the critical
frequency will match a bending mode of the bamer
and will be able to pass through the bamer
This phenomenon is called coincidence.
74


Isolation Coincidence
When Coincidence occurs, efficient sound
transfer from one side of the bamer to the
other occurs
This creates a Coincidence Dip in the TL
data and can effect STC greatly
Coincidence allows for efficient sound transfer from
one side of the barrier to the other
A noticeable dip m the TL data can be seen. This is
referred to as a coincidence dip. Because it can be so
large, the coincidence dip is what determines the STC
ratings for most barriers.
Isolation Coincidence
Transmission loss data showing the three regions and
coincidence dips of bamers with different types of
damping.
37
38
Isolation Coincidence
Material Thickness Thickness Frequency (in) (Hz) '
Brick 200 8 1 115
Glass 3 125 5000
Gypsum 13 .5 2500
Plywood 13 . .5 1700
Steel 125 4000
The effect of coincidence on STC.
Coincidence frequencies of common building
materials
39
40
75


Structure Borne Noise
Noise from machines like Air Conditioners
and Fans may send vibrations through the
structure and create noise
I Mechanical |
I Equipment |
! I
k k
Transmitted Noise and Vibration
Mechanical equipment like HVAC wits can send
vibrations through the structure and cause noise
To isolate from noise, mechanical eqiupment can be
decoupled from the structure using springs and
damping pads
The springs Mill absorb the mechanical vibration and
prevent it's transfer to the structure
Mass and Decoupling
It's ideal to stop the transmission of sound
using materials with very different
propagation properties
- Block sound traveling in air with concrete
- Block sound traveling in concrete with air
A combination of Mass and Decoupling
will result in effective isolation
Room within Room construction!
The most efficient way of stopping the transmission
of soimd is by using matenals with very different
propagation properties than what the sound is being
transmitted with. This is called decoupling.
For example, to block sound traveling in air. use a
barrier made of concrete. To block sound traveling
through concrete, use a barrier of air
A clever combination of mass and decoupling will
result in the most effective isolation.
This type of thinking leads directly to Room within
Room construction.
In room within room construction, inner rooms are
built inside of outer shell rooms and neither room is
connected to the other.
This allows for maximum decoupling.
Combined together with massive separating walls,
this creates the most effective isolation solution.
76


Multi-Layer Walls
Double Wall System
ca*. c> 1
Wall J Wall 2
Air Gap, Ideally, the walls should be as massive as possible and air space as large as
Double Wall System between two moms that are relatively quiet or don't need much pomible/needed. Available space and money will dictate deagn. however.
*' i
Multi-Layer Walls
Walls built on the concept of room within room
construction can be double or triple (or more) layers
thick
In double wall systems an air gap separates the walls
between the two adjacent rooms. The walls
themselves might be built out of multiple layers of
sheetrock, cinder block, or poured concrete
depending on the STC rating needed.
Tnple wall systems have an inner wall between two
rooms that is decoupled from both rooms
Most often, these walls are structural and are part of
the outer shell structure
A triple wall is a more effective barrier between two
rooms with high noise levels, such as two control
rooms in one common building
Floor Systems
There are two ways to isolate floors
- Spilt Slab Constniction
- Floating Floor Constniction
Split slab provides maximum isolation
- Cannot be done on any floor other than ground
level
Floating Floor is good alternative
Floor Systems
Split Slab
Foundation
Room IN.
---\
Ground^"
^yRoom 2
The poured cement floor is cut at the boundary of the
two rooms and Styrofoam is inserted to insure i solan on
Can only be done 01 the ground level (obviously).
46
There are two ways to isolate inner room floors with
the outer shell floors
split slab construction
-Floating floor construction
Split slab construction provides maximum isolation it
can only be done on the ground level floor
Floating floor construction is a good alternative but
not as effective as split slab.
The cement slabs of a floor are cut in split slab
construction. This provides maximum isolation
because sound is not easily transmitted through the
ground.
This can only be accomplished on the ground level
Attempting to cut the floor on an elevated level of a
building will cause the structure to collapse.
77


Floor Systems
Flatting ^ Air Gap
Fkxx Isolating
Room 1. Material'

Isolating
Matenal
An isolating matenal is put down between the stmcturm!
Door and the flooring for the individual rooms
Floor Systems
Roll-out floor isolation product
imbedded in
Flooring is put an top of roll-out
insulation and isolated from the floor
below by isolators
Multiple layers of plywood should
be put down to create mass
An isolating matenal is placed between the inner room and outer shell on a floating floor construction. Kinetics Noise Control manufactures a unique floor isolation system
Compressed rubber isolators are typically used as the isolating matenal Isolators are imbedded in an isolation matenal that can be rolled out. Correct spacing is already taken care of.
Multiple layers of plywood and/or sheetrock are put down on top of the isolators to make the floors rigid and massive Images from products by Kinetics Noise Control
49
Ceiling Systems
There are two ways to isolate ceilings
- Lid construction
- Hanging construction
Lid construction provides maximum isolation
- Is only possible with small-medium size rooms
Hanging construction is a good alternative
- Tricky to do and expensive
Ceiling Systems
so
There are two ways to isolate ceilings
-Lid construction
-Hanging construction
Lid construction provides the best isolation but is
only feasible with small to medium sized rooms.
Hanging construction is a good alternative but is
tricky to design and can get expensive
Ceilings with lid construction are supported by the
inner walls and do not touch the outer shell.
For larger rooms, the weight of the ceiling combined
with the weight of the HV AC and lighting systems is
often too great for the inner walls to support This is
why lid construction is usually used only for small to
medium sized rooms.
si
52
78


WM l*stn.innli U
Existing Ceiling
Ceiling Systems
Hanging Caafliuc&on
J l l x
---^--. V / ^
Room I omlm^Spniig \vLxxS
* Ceiling of the isolated room is hung from
existing ceiling by spring isolators.
Method can be costly and difficult to set up
- Exact weight of isolated ceiling needs to be
calculated for proper spring isolator selection

Ceiling Systems
Hnging Constmctiai
Typical ceiling spring isolator.
Come in all different spring selections
Can be hung from metal rods to hang
from extra high ceilings
Hanging construction makes use of spring isolators to Spring isolators come in all different spring sizes and
hang the inner room ceiling from the outer shell The inner ceiling makes contact to the outer shell only configurations
through spnng isolators and is never rigidly connected. Images from products by Kinetics Noise Control
This method is effective but is also costly and difficult to set up. The exact weight of the ceiling needs to be calculated for proper spnng isolator selection.
53
Doors
1 Effective, leak-proof doors are necessary
1 The more massive the door...
- The better the STC Rating
- The more expensive
1 Choose a door to meet design criteria
This is what a complete isolation solution might look like. This particular solution uses products manufactured by Kinetics Noise Control. Effective leak-proof doors are absolutely necessary in good isolation design.
Images from products by Kinetics Noise Control Acoustical doors are often very massive and. in turn, very pricey.
When shopping for an acoustical door, only choose a door to meet your design criteria Overkill Mill only cost more money-
55
79


Ml . j-- -
Doors Windows
Cam Lift Hinges will.. -Lift and drop the door upon opening and closing -Allow a tight bottom seal (~drop seal") Mike the door self closing __ Effective bottom seals are necessarv and Many different types of ~ windows available ocm Installation is critical! f; Gaps around window frame mil make a high STC window useless

The best acoustical doors use cam-lift hinges and have tight seals around all four edges of the door. There are many different types of windows available with high STC ratings. You may also elect to build your own In either case, installation is critical
Cam-lift hinges lift and drop the door as is opens and doses for an effective bottom seal and make the door self closing without the use of hydraulics Gaps around the window frame will make a high STC window useless.
The bottom seal of a door is the most important seal that is also the most overlooked They have a tendency to break or wear out on high traffic doors. Images from products by Acoustical Surfaces, Inc
Images from products by Acoustical Solutions and Kinetics Noise Control
57
$8
HVAC
Can make any quiet room noisy if not designed
properly
Reduce airflow rate at Supply and Return ducts by
making them large
Ovenue ducts allow air to move slowlv aid provide
room for insulation
- Inline Air Silencers
Or just turn it off!! Why spend money if you dont
need to? -Very acceptable cial solution to a
technical problem -ktn&oryk
HVAC can make any quiet room sound noisy if it is
not designed properly
-to reduce airflow noise, reduce the airflow rate at
supply and return ducts by making them large
-Ovesized ducts can be lined with insulation and
allow the air to move slowly, reducing turbulence
noise
-Air silencers can be placed along ductwork for
increased isolation
Or, if its an option, turn it off while recording!
Soundlocks
* In professional situations, every' room should
connect via a soundlock
* The Soundlock is a completely isolated room
Sometimes can also be used u vocal booth
All HVAC. wiring, etc. should be run thru the
soundlock
- Adds an additional boundary of isolation between
An often overlooked design element that greatly
helps to reduce noise between rooms is the
soundlock.
The soundlock is completely a completely isolated
room itself, just like the other studio and control
rooms. Because of this, they sometimes can double as
an extra vocal booth.
All HVAC, wiring, cable troughs, etc. should be run
through the soundlock before entering another room
This provides another boundary of isolation
80


The soundlock seperates Control room A from Studio
A-B
The main hallway is acting as the soundlock from
Control room B. This is an effective solution if the
hallway is quiet.
Image courtesy of John Storyk, Walters-Storyk
Design Group:
Storyk, J. (2006). Architecture and Acoustics of
Critical Listening Environments. Presented January
27-29 and February 3-4,2006, at the University of
Colorado at Denver.


Homework #6
Isolation
(answers in italics)
1) Whats the easiest way to ensure a quiet studio?
Build the studio in a quiet location.
2) What are 3 common ways to describe the noisiness level of a room?
Noise Criteria (NC), Preferred Noise Criteria (PNC), and Noise Rating (NR) ratings.
3) Define Transmission Loss
Transmission Loss is the reduction of SPL from the passage through a barrier.
TL = f-L2 + lOlog
A
where
L, is the SPL in Source Room
L2 is the SPL in Reciever Room
S is total surface area of the Barrier
A is the total absorption of Reciever Room in Sabines (Sab)
(A is also known as ^ S a)
4) There is a 8 by 20 barrier (wall) that has TL of 52 dB separating two rooms. One
room has a noise source playing at 90 dB. The second room has 3000 sabins of
absorption and is hearing the noise, but at a lower level. At what level is the second
room hearing the noise?
TL = f L2 +101og
A
L2 = 25dB
5) What is Sound Transmission Class and how does it differ from Transmission Loss?
STC is a TL vs frequency curve that is represented be a single number.
STC looks at TL over a wide range of frequencies whereas TL is only validfor a
single frequency.
82


6) What are the procedures of determining STC?
An STC curve has a :
3 dB per 1/3 octave rollofffrom 125-400 Hz
1 dB per 1/3 octave rolloff from 400-1250 Hz
Flat line from 1250-4000 Hz
A 1/3 octave band room reading is fitted on the same graph as the STC curve. The
STC curve is slid up the graph until
The difference between one 1/3 octave band reading and the STC curve
reaches 8 dB
The sum of differences between the 1/3 octave band reading and the STC
curve reaches 32 dB
The STC rating is given by the curves position at 500 Hz.
7) A barrier between 2 rooms is made up of 3 walls. Wall 1 has an STC of 48. Wall 2
has an STC of 40. Wall 3 has an STC of 39. What is the combined STC rating for the
whole barrier?
STC, STC2 STC
STCUI = 101og(£l0 10 +10 10 +... + 10 10 )
STC = 49
8) What is coincidence as it relates to STC and how can it be controlled?
Coincidence occurs when the wavelength of sound matches the wavelength of the
bending modes of a barrier. This allows the sound to efficiently pass through the
barrier and creates a coincidence dip that effects the TL loss and the STC rating.
9) What effect do small holes for wires and small gaps around door edges have on
STC, if any?
Small holes and leaks around door edges have an enormous impact on STC.
The TL for a leaky door is 7-12 dB worse than a properly sealed door.
A hole of 0.1% of the total area of a barrier can easily bring the STC rating for the
barrier from 60 to 30.
83


10) Mass and Decoupling are the two necessary ingredients for isolation acoustics.
What does this mean?
Materials with mass effectively prohibit the transmission of sound in air. Mass that is
decoupled from other structures effectively prohibits the transmission of sound
through structures.
Mass and decoupling leads to room within room design.
11) How would you isolate a floor:
a) On the ground level of a building?
b) On the 3 rd story of an apartment complex?
c) Which is more effective?
a) isolate the floor on the ground level using split slab construction
b) isolate the floor on the 3rd story using floating floor construction
c) split slab construction is more effective at isolation
12) Describe the two ways to isolate the ceiling of a studio.
Use lid construction where the inner ceiling is completely supported between the
inner walls.
Use hanging construction where the inner ceiling is supported between the inner
walls as well as using springs that connect to the outer ceiling.
13) What are the components that make up a good acoustical door design?
Massive
- Leak proof
o Cam lift hinges
o Bottom seal in working order
o Door jams sealed
o No holes
84


4.7 Internal Acoustics and Homework 7
The internal acoustics topic covers what most of the students would have
previously considered the whole of the acoustic design course. Because of this, they
may already have preconceived notions or be misinformed about acoustic topics,
namely the use of absorption. The subjects covered in this topic include:
Wave interaction with objects
Specular and diffuse reflection
Comb filtering
Absorption and the absorption coefficient
The effect of thickness, density, and airspace on absorption
The quarter wavelength criteria for effective absorption
Low frequency absorption
Resonators and diaphragmatic absorbers
Polycylindricals as low frequency absorbers and high frequency diffusers
Diffusion and Quadratic Residue Diffusers
Modal analysis
Mode stacking and appropriate room ratios
Mode excitation due to speaker placement
The difference between raytrace and modal frequencies
85


Internal Acoustics
Acoustic Fundamentals of Critical Listening and This topic will cover
Performance Spaces Topic 7 Internal Acoustics -how waves interact with objects
Daniel Hicks -Specular and diffuse reflections and the comb filtenng phenomenon
All pictures and images are creations of the author -Absorptive materials, absorption coefficients, the
unless otherwise specified. effect of thickness, density, and airspace, and low frequency absorption
What well cover
Wave Interaction with Objects
Reflection
Specular vj DifTtise
Comb Filienag
Absorption
Absorption Coefficient
Thickness. Density, end Airspace
L4 cntena
- Low Frequency Absorption
What well cover
Diffusion
Polycylindricals, QRD. DiffraetaJs
Rev erberation Time
Modal Analysis
- Rayleigh Equation
Mode stacking and packing
Room size and ratios
- Mode excitation
Mode vs Raytrace Frequencies
Wave Interaction with Objects
> An object will influence the travel of a
sound wave depending on:
- The size of the object in relation to the
wavelength of sound
-Diffusion by poycylindricals. quardratic residue
diffusors. and diffractals
-The reverberation time of rooms
-Modal analysis and proper room ratios
-How to differentiate between modal and raytrace
frequencies
An object will influence the travel of a sound wave
depending on the size of the object in relation to the
wavelength of the sound.
86


There are 3 things that can happen when sound
comes into contact with an object
-Specular Reflection
Diffuse reflection
Absorption
Sound energy cannot be created or destroyed, only
converted from one form to another
There are two types of reflection
-Specular
-Diffuse
in specular reflection, the angle that the sound hits an
object is the angle that sound is reflected off of the
object.
In diffuse reflection, sound will hit an object and then
be scattered in all different directions
6
Reflection
Specular reflections arriving within 40ms of
each other are perceived as coming from the
same source
- Remember. Haas Effect
These reflected sounds are combined
together and can create a special type of
destructive interference called..
Comb Filtenng
Reflection
Comb Filtenng happens when the first
reflection arrives within 40 ms of the direct
sound
First reflection can be off of any hard
surface
- Console
- Nearby wall
- Floor or Ceiling
Specular reflections amve within 40 ms of each other
and with less than 10 dB m level difference are
perceived as coming from the same source.
These reflected sounds that are combined together
can create a special type of destructive interference
called Comb Filtering.
Comb Filtenng occurs when a reflected sound
combines with the direct sound
The first reflection can be off of any hard surface in
between the source and receiver such as
-Console
-Nearby wall
-Floor or ceiling
87


Example of possible reflection situations
Reflection
The reflected and direct sound combine and create a
comb-looking type of interference.
This can be very' unpleasant to listen to.
Image courtesy of Wilson Audio:
Wilson Audio Room Acoustics. Retrieved May 9,
2006 from
http://www.wilsonaudio.com/technotes/roomacousUc
s.shtm)
Absorption
10
Absorption Coefficient
Absorptive materials dissipate sound energy
by turning it into heat energy
A materials absorption is described by a
number, usually between 0 and 1, called the
absorption coefficient
- Usually given for each octave band
The Absorption Coefficient is denoted by
the letter o "alpha
a = 1.0 (completely absorptive)
a 0.0 (no absorption)
Absorption coefficients can occasionally be
greater than I due to 'extra' absorption of
the materials edges and/or backing
Absorptive matenals dissipate sound by turning it
into heat energy
A matenals absorption is descnbed by a single
number called the absorption coefficient. The
absorption coefficient is usually between 0 and 1 and
given for each octave band.
The absorption coefficient is denoted by the greek
letter alpha
A coefficient of 0 means that the material is
completely reflective (no absorption). A coefficient
of 1 means that the matenal is completely absorptive
(no reflection)
It is possible for a matenal to have a number greater
than 1 although it is not typical.
li
12
88


Absorption Coefficient
' For calculating absorption in a room, it is
often helpful to talk about total absorption
of a surface
TotalAbsorption = S a (sabins)
where
S is the surface area of the surface
a is the Absorption Coefficient
Absorption Thickness
1 Materials become more absorptive when
they are thicker
- Higher frequencies are effected more than lower
It is often helpful to talk about the total absorption Materials become more absorptive as thickness
of a surface. increases.
Total absorption is the absorption coefficient Higher frequencies are effected more than lower
multiplied by the surface area of the surface frequencies due to thickness.
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Absorption Thickness Density and Airspace
r
/" / T / / (SOiwk) Density has very little effect on Absorption
\ \ 1 | / / (29r>m) - Denser materials absorb slightly better at high frequencies and slightly worse at low frequencies
An airspace behind the absorber is a good way to increase low frequency absorption
of IrfstSuryk. WOl- Storyk Dmfn Ore?
MC 500 tooe 2000 40 Fqu*nqr(Ht)
Graph showing the effect of thickness on absorption Density has very little effect on absorption
coefficient. An airspace behind an absorber is a good way to
Graph courtesy of John Storyk. Walters-Storyk increase the low frequency absorption. This is due to
Design Group: the L/4 catena.
Storyk, J. (2006). Architecture and Acoustics of Critical Listening Environments. Presented January 27-29 and February 3-4, 2006, at the University of Colorado at Denver
IS
89


The bandwidth and frequency that an absorber is
effective is controlled by the L/4 criteria
At one-quarter of a wavelength, particle displacement
for a sound wave is at a maximum and particle
velocity is at a minimum. This is a good spot to
"trap the particles of air and stop the pressure wave
from moving
To effectively absorb a specific frequency, place the
absorber L/4 away from the boundary
This can be done by using a spacer behind the
absorber.
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For maximum absorption, combine the effects of the
L/4 airspace with increased thickness.
This will also broaden the frequency range which the
absorber is effective.
Absorption L/4
Fmquancy Wauatangtti
c* 1130R/S
31 S At wsni iU b
I S3 Hr 1790 ft 4 48 rt
j 125 Hr 900 n 225 ft
I 250 Hr 4 52 It 1 13 ft
500 Hr 2 26 ft 6 78 m
1 Wtt 1 13 It 339 n
2 Mr 6 78 m 1 70 It
4 339 m 0 85 n
B tttt 1 70 m 043 n
16 kHz 085 n 021 *>
Low frequencies require their own approach for absorption
A table showing the L/4 airspace required for specific
frequencies.
Notice that the L/4 distances for low frequencies are
quite large. Because of this, it is better to approach
low frequency absorption from a different
perspective
is
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20
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Absorption Low Frequencies
Low frequencies are most often treated by
'resonant' or reactive' absorbers
- Resonators
Helmholtz Resonators
Performed Pwd Aheorbers
Slat Abeorfeen
- Diaphragmatic
Membrane Absorbers
Potycylindncals
Low frequencies are most often treated by resonant
or reactive absorbers.
These are most often helmhoitz resonators or
membrane absorbers
i
Helmholtz Resonators
By blowing air across an empty bottle or J
jug, a specific frequency is excited j
- The mass of air in the neck of the bottle reacts ]
with the springy air in the cavity of the bottle |
Resonators rely on the same concept to 1
absorb low frequency sound
- Sound that is not absorbed, is reradiatcd in a
diffuse partem
______________________________________________I
When air moves across an empty bottle or jug. a
specific frequency is excited. This is the same
concept that applies to pipe organs and many other
musical instruments
Resonators rely on the same concept to absorb sound.
Perforated Panel Absorbers
1 Perforated hardboard or plywood spaced at
a distance away from the wall
- Perforations act as the 'neck' of the bottle
- Airspace acts as the bottle cavity
- Glass fiber on the wall behind absorber will
broaden the absorption curve

/ the effected fratyutncy
pttlhe perfonuan perccrttfc
i it (panel Ihjcknees) < 0 SQinie ihamsta) si achat
A it depth of ertpecc in indies
A perforated panel absorber is a type of resonator
A panel that is perforated with hundreds of small
holes is placed at a hard wall or other boundary with
an airspace behind it.
The perforations act as the 'neck' of the bottle and
the airspace acts as the bottle cavity.
Glass fiber placed on the wall behind the panel will
broaden the absorption curve.
Slat Absorbers
Slats or stnps of wood spaced with a gap
between them and at a wall airspace
- Mass of air between the slats reacts with the air
mass created from the airspace

what
/ the effected fraquoicy
f a the pertareben percentage
D w the ductalnir af the del in m
A w depth ef ainpeee in inches
Slat absorbers are similar to perforated panel
absorbers
Stnps of wood are spaced with a gap between them.
The mass of air between the slats reacts with the
mass of air behind the panel
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Membrane Absorbers
Polycylindricals
A thin membrane will naturally resonate
and absorb sound due to factional heat loss
where
f is the frequency of resonance
m is the Ib/sq ft of panel
d is depth of airspace in inches
Thin membranes naturally resonate at tow
frequencies.
If these are placed in the correct location in a room,
they are effective at absorbing low frequencies.

Polycylindncals are membranes that are
bowed or curv ed
They have a unique absorption curve
because of the naturally changing airspace
- Low frequency absorption can be enhanced by
filling the cavity with glass fiber
Polycylindricals are membranes that are bowed.
The have a unique absorption curve because of the
naturally changing airspace behind them. Again, the
absorption curve can be broadened if the cavity is
filled with glass fiber.
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Polycylindncals
Polycylindncals are also unique in that they
can also be used to diffuse high frequencies
Polycylindricals are also unique in that they will
diffuse higher frequencies.
They can then be used as both a low frequency
absorber and a high frequency diffuser
Polycylindricals
Image eornmav lain Smiyk. WaJun-Storyk Daaign Qmg
Polycylindncals along the wall of a conference room
at Mercury Records
Design by John Storyk
Image courtesy of John Storyk, Walters-Storyk
Design Group.
Storyk, J. (2006). Architecture and Acoustics of
Critical Listening Environments Presented January
27-29 and February 3-4. 2006, at the University of
Colorado at Denver.
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