www.elsolucionario.org
`
`Page 1 of 43
`Page 1 of 43
`Page 1 of 43
`
`HAPTIC EX2005
`
`

`

`GLOSSARY OF SYMBOLS
`
`This list identifies some symbols that are not necessarily defined every time they
`appear in the text.
`
`a
`
`C N E L
`
`acceleration; absorption
`coefficient (dB per
`distance); Sabine
`absorptivity
`random-incidence energy
`absorption coefficient
`sound absorption
`array gain
`loss per bounce; decay
`parameter
`beam pattern
`magnetic field;
`susceptance
`bottom loss
`adiabatic bulk modulus
`isothermal bulk modulus
`speed of sound
`group speed
`phase speed
`electrical capacitance;
`acoustic compliance;
`heat capacity
`heat capacity at constant
`pressure
`specific heat at constant
`pressure
`heat capacity at constant
`volume
`specific heat at constant
`volume
`community noise
`equivalent level (dBA)
`detection index
`
`d'
`D
`DI
`
`DNL
`DT
`
`9
`
`detectability index
`
`directivity; dipole strength
`
`directivity index
`
`detected noise level
`detection threshold
`
`diffraction factor
`specific energy
`
`total energy
`
`kinetic energy
`potential energy
`echo level
`time-averaged energy
`density
`instantaneous energy
`density
`instantaneous force;
`frequency (Hz)
`resonance frequency
`
`upper, lower half-power
`frequencies
`peak force amplitude;
`frequency (kHz)
`effective force amplitude
`spectral density of a
`transient function;
`sound-speed gradient;
`acceleration of gravity;
`aperture function
`
`conductance
`adiabatic shear modulus
`specific enthalpy
`directional factor
`
`Page 2 of 43
`
`

`

`LTpN
`
`L,
`
`LNP
`m
`m,
`M
`
`population function
`time-averaged acoustic
`intensity; current,
`effective current
`amplitude
`reference acoustic
`intensity
`instantaneous acoustic
`intensity
`impact isolation class
`intensity level
`intensity spectrum level
`
`.9 (t)
`
`.Mr@
`
`P
`P
`
`P,
`
`Prcf
`
`PR
`Pr
`P S L
`P T S
`Y
`Po
`
`tone-corrected perceived
`noise level
`x-percentile-exceeded
`sound level (dBA, fast)
`noise pollution level (dBA)
`mass
`radiation mass
`acoustic inertance;
`bending moment;
`molecular weight;
`acoustic Mach number,
`flow Mach number
`.M
`microphone sensitivity
`time-averaged spectral
`.MY microphone sensitivity
`density of intensity
`level
`instantaneous spectral
`reference microphone
`density of intensity
`sensitivity
`impulse
`N
`loudness (sone)
`wave number
`NCB balanced noise criterion
`propagation vector
`curves
`Boltzmann's constant
`NEF
`noise exposure forecast
`coupling coefficients
`www.SolutionManual.info
`NL
`noise level
`discontinuity distance
`N R
`noise reduction
`inductance
`NSL noise spectrum level
`A-weighted sound level
`( d B 4
`C-weighted sound level
`(dBC)
`daytime average sound
`level (dBA)
`day-night averaged sound
`level (dBA)
`evening average sound
`level (dBA)
`equivalent continuous
`sound level (dBA)
`noise exposure level
`(dBA)
`effective perceived noise
`level
`hourly average sound level
`( d B 4
`intensity level re lo-''
`W/m2
`loudness level (phon)
`night average sound level
`( d B 4
`
`acoustic pressure
`peak acoustic pressure
`amplitude
`effective acoustic pressure
`amplitude
`reference effective acoustic
`pressure amplitude
`privacy rating
`Prandtl number
`pressure spectrum level
`permanent threshold shift
`hydrostatic pressure
`equilibrium hydrostatic
`pressure
`
`9
`
`charge; source strength
`density; thermal energy;
`scaled acoustic pressure
`( p l POC')
`quality factor; source
`strength (amplitude of
`volume velocity)
`(continued on back endpapers)
`
`Q
`
`Page 3 of 43
`
`

`

`FUNDAMENTALS OF
`ACOUSTICS
`
`Fourth Edition
`
`LAWRENCE E. KINSLER
`Late Professor Emeritus
`Naval Postgraduate School
`
`AUSTIN R. FREY
`www.SolutionManual.info
`Late Professor Emeritus
`Naval Postgraduate School
`
`ALAN B. COPPENS
`Black Mountain
`North Carolina
`
`JAMES V. SANDERS
`Associate Professor of Physics
`Naval Postgraduate School
`
`NewYork
`
`John Wiley 6 Sons, Inc.
`Chichester Weinheim
`Brisbane
`
`Singapore
`
`Toronto
`
`Page 4 of 43
`
`

`

`With grateful thanks to our wives,
`Linda Miles Coppens and Marilyn Sanders,
`for their unflagging support and gen tie patience.
`
`ACQUISITIONS EDITOR
`
`Stuart Johnson
`
`MARKETING MANAGER
`
`Sue Lyons
`
`PRODUCTION EDITOR
`
`Barbara Russiello
`
`SENIOR DESIGNER
`
`Kevin Murphy
`
`ELECTRONIC ILLUSTRATIONS
`
`Publication Services, Inc.
`
`This book was set in 10/12 Palatino by Publication Services, Inc. and printed and bound by Hamilton
`Press. The cover was printed by Hamilton Press.
`
`This book is printed on acid-free paper.
`
`Copyright 20000 John Wiley & Sons, Inc. All rights reserved.
`No part of this publication may be reproduced, stored in a retrieval system or transmitted in any
`form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise,
`except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without either
`the prior written permission of the Publisher, or authorization through payment of the appropriate
`per-copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, (508)
`750-8400, fax (508) 750-4470. Requests to the Publisher for permission should be addressed to the
`Permissions Department, John Wiley & Sons, Inc., 605 Third Avenue, New York, NY 10158-0012,
`(212) 850-6011, fax (212) 850-6008, E-mail: PERMREQ@WILEY.COM. To order books or for customer
`service please call l(800)-225-5945.
`
`Library of Congress Cataloging-in-Publication Data:
`Fundamentals of acoustics / Lawrence E. Kinsler. . .[et al.1.4th ed.
`p.cm.
`Includes index.
`1. Sound-waves. 2. Sound-Equipment and supplies. 3. Architectural acoustics. I.
`Kinsler. Lawrence E.
`
`5 3 4 4 ~ 2 1
`
`QC243 .F86 2000
`ISBN 0-471-84789-5
`Printed in the United States of America
`1 0 9 8 7 6 5 4 3 2
`
`Page 5 of 43
`
`

`

`www.elsolucionario.org
`
`PREFACE
`
`Credit for the longevity of this work belongs to the original two authors, Lawrence
`Kinsler and Austin Frey, both of whom have now passed away. When Austin
`entrusted us with the preparation of the third edition, our goal was to update
`the text while maintaining the spirit of the first two editions. The continued
`acceptance of this book in advanced undergraduate and introductory graduate
`www.SolutionManual.info
`courses suggests that this goal was met. For this fourth edition, we have continued
`this updating and have added new material.
`Considerable effort has been made to provide more homework problems. The
`total number has been increased from about 300 in the previous editions to over
`700 in this edition. The availability of desktop computers now makes it possible for
`students to investigate many acoustic problems that were previously too tedious
`and time consuming for classroom use. Included in this category are investigations
`of the limits of validity of approximate solutions and numerically based studies of
`the effects of varying the various parameters in a problem. To take advantage of
`this new tool, we have added a great number of problems (usually marked with a
`suffix "C" ) where the student may be expected to use or write computer programs.
`Any convenient programming language should work, but one with good graphing
`software will make things easier. Doing these problems should develop a greater
`appreciation of acoustics and its applications while also enhancing computer skills.
`The following additional changes have been made in the fourth edition:
`(1) As an organizational aid to the student, and to save instructors some time,
`equations, figures, tables, and homework problems are all now numbered by chap-
`ter and section. Although appearing somewhat more cumbersome, we believe the
`organizational advantages far outweigh the disadvantages. (2) The discussion of
`transmitter and receiver sensitivity has been moved to Chapter 5 to facilitate early
`incorporation of microphones in any accompanying laboratory. (3) The chapters
`on absorption and sources have been interchanged so that the discussion of
`beam patterns precedes the more sophisticated discussion of absorption effects.
`(4) Derivations from the diffusion equation of the effects of thermal conductivity
`on the attenuation of waves in the free field and in pipes have been added to
`the chapter on absorption. (5) The discussions of normal modes and waveguides
`
`Page 6 of 43
`
`

`

`iv
`
`PREFACE
`
`have been collected into a single chapter and have been expanded to include
`normal modes in cylindrical and spherical cavities and propagation in layers.
`(6) Considerations of transient excitations and orthonormality have been en-
`hanced. (7) Two new chapters have been added to illustrate how the principles
`of acoustics can be applied to topics that are not normally covered in an under-
`graduate course. These chapters, on finite-amplitude acoustics and shock waves,
`are not meant to survey developments in these fields. They are intended to intro-
`duce the relevant underlying acoustic principles and to demonstrate how the funda-
`mentals of acoustics can be extended to certain more complicated problems.
`We have selected these examples from our own areas of teaching and research.
`(8) The appendixes have been enhanced to provide more information on physical
`constants, elementary transcendental functions (equations, tables, and figures),
`elements of thermodynamics, and elasticity and viscosity.
`New materials are frequently at a somewhat more advanced level. As in the
`third edition, we have indicated with asterisks in the Contents those sections in
`each chapter that can be eliminated in a lower-level introductory course. Such a
`course can be based on the first five or six chapters with selected topics from the
`seventh and eighth. Beyond these, the remaining chapters are independent of each
`other (with only a couple of exceptions that can be dealt with quite easily), so that
`topics of interest can be chosen at will.
`With the advent of the handheld calculator, it was no longer necessary for text-
`books to include tables for trigonometric, exponential, and logarithmic functions.
`While the availability of desktop calculators and current mathematical software
`makes it unnecessary to include tables of more complicated functions (Bessel
`functions, etc.), until handheld calculators have these functions programmed into
`them, tables are still useful. However, students are encouraged to use their desktop
`calculators to make fine-grained tables for the functions found in the appendixes.
`In addition, they will find it useful to create tables for such things as the shock
`parameters in Chapter 17.
`From time to time we will be posting updated information on our web site:
`www.wiley.com/college/kinsler. At this site you will also be able to send us
`messages. We welcome you to do so.
`We would like to express our appreciation to those who have educated us,
`corrected many of our misconceptions, and aided us: our coauthors Austin R. Frey
`and Lawrence E. Kinsler; our mentors James Mcgrath, Edwin Ressler, Robert T.
`Beyer, and A. 0. Williams; our colleagues 0. B. Wilson, Anthony Atchley, Steve
`Baker, and Wayne M. Wright; and our many students, including Lt. Thomas Green
`(who programmed many of the computer problems in Chapters 1-15) and L. Miles.
`Finally, we offer out heartfelt thanks for their help, cooperation, advice, and
`guidance to those at John Wiley & Sons who were instrumental in preparing
`this edition of the book: physics editor Stuart Johnson, production editor Barbara
`Russiello, designer Kevin Murphy, editorial program assistants Cathy Donovan
`and Tom Hempstead, as well as to Christina della Bartolomea who copy edited
`the manuscript and Gloria Hamilton who proofread the galleys.
`
`Alan B. Coppens
`Black Mountain, NC
`
`James V. Sanders
`Monterey, CA
`
`Page 7 of 43
`
`

`

`CONTENTS
`
`CHAPTER 1
`FUNDAMENTALS OF VIBRATION
`
`1.1 Introduction
`
`1
`
`1.9 Power Relations
`
`14
`
`1.2 The Simple Oscillator
`
`2
`
`1.3 Initial Conditions
`
`3
`
`1.4 Energy of Vibration
`
`5
`
`1.5 Complex Exponential Method
`of Solution
`5
`
`1.6 Damped Oscillations
`
`8
`
`1.7 Forced Oscillations
`
`11
`
`1.8 Transient Response
`of an Oscillator
`13
`
`www.SolutionManual.info
`
`1.10 Mechanical Resonance
`1.11 Mechanical Resonance
`and Frequency
`17
`"1.12 ~ q u i v a l e n t Electrical Circuits
`for Oscillators
`19
`
`15
`
`1.13 Linear Combinations of Simple
`Harmonic Vibrations
`22
`1.14 Analysis of Complex Vibrations
`by Fourier's Theorem
`24
`
`*1.15 The Fourier Transform
`
`26
`
`CHAPTER 2
`TRANSVERSE MOTION: THE VIBRATING STRING
`
`2.1 Vibrations
`of Extended Systems
`2.2 Transverse Waves
`on a String
`37
`2.3 The One-Dimensional
`Wave Equation
`38
`2.4 General Solution
`of the Wave Equation
`
`37
`
`39
`
`2.5 Wave Nature
`of the General Solution
`2.6 Initial Values and
`Boundary Conditions
`
`40
`
`41
`
`2.7 Reflection a t a Boundary
`
`41
`
`2.8 Forced Vibration
`of a n Infinite String
`
`42
`
`2.9 Forced Vibration of a String
`of Finite Length
`46
`
`(a) The Forced,
`Fixed String
`
`46
`
`*(b) The Forced,
`Mass-Loaded String
`
`49
`
`*(c) The Forced, Resistance-
`Loaded String
`51
`
`Page 8 of 43
`
`

`

`www.elsolucionario.org
`
`CONTENTS
`
`52
`
`2.10 Normal Modes
`of the Fixed,
`Fixed String
`(a) A Plucked String 54
`(b) A Struck String
`*2.11 Effects of More Realistic
`Boundary Conditions
`on the Freely Vibrating
`String 54
`
`54
`
`(a) The Fixed,
`Mass-Loaded String
`
`55
`
`CHAPTER 3
`VIBRATIONS OF BARS
`
`3 . 1 Longitudinal Vibrations
`of a Bar
`68
`
`3.2 Longitudinal Strain 68
`3.3 Longitudinal
`Wave Equation
`3.4 Simple Boundary
`Conditions
`71
`
`69
`
`73
`
`3.5 The Free, Mass-Loaded Bar
`*3.6 The Freely Vibrating Bar:
`General Boundary
`Conditions
`75
`*3.7 Forced Vibrations of a Bar:
`Resonance and Antiresonance
`Revisited
`76
`
`(b) The Fixed, Resistance-
`Loaded String
`56
`
`(c) The Fixed,
`Fixed Damped String 57
`2.12 Energy of Vibration
`of a String 58
`*2.13 Normal Modes,
`Fourier's Theorem,
`and Orthogonality 60
`2.14 Overtones
`and Harmonics
`
`62
`
`*3.8 Transverse Vibrations
`of a Bar
`78
`
`*3.9 Transverse
`Wave Equation
`80
`*3.10 Boundary Conditions
`(a) Clamped End
`
`82
`
`82
`
`(b) Free End
`
`82
`
`(c) Simply
`Supported End
`
`82
`
`*3.11 Bar Clamped at One End
`
`83
`
`*3.12 Bar Free at Both Ends
`*3.13 Torsional Waves
`on a Bar
`86
`
`84
`
`CHAPTER 4
`THE TWO-DIMENSIONAL WAVE EQUATION:
`VIBRATIONS OF MEMBRANES A N D PLATES
`
`4 . 1 Vibrations
`of a Plane Surface
`4.2 The Wave Equation
`for a Stretched Membrane 91
`
`91
`
`4.3 Free Vibrations
`of a Rectangular Membrane
`with Fixed Rim
`93
`
`4 . 4 Free Vibrations
`of a Circular Membrane
`with Fixed Rim
`95
`
`4.5 Symmetric Vibrations
`of a Circular Membrane
`with Fixed Rim
`98
`*4.6 The Damped, Freely Vibrating
`Membrane
`99
`
`*4.7 The Kettledrum
`*4.8 Forced Vibration
`of a Membrane
`
`100
`
`102
`
`*4.9 The Diaphragm
`of a Condenser
`Microphone
`103
`
`*4.10 Normal Modes
`of Membranes
`
`104
`
`(a) The Rectangular Membrane
`with Fixed Rim
`I05
`
`(b) The Circular Membrane
`with Fixed Rim
`106
`
`*4.11 Vibration
`of Thin Plates
`
`107
`
`Page 9 of 43
`
`

`

`CONTENTS
`
`vii
`
`CHAPTER 5
`THE ACOUSTIC WAVE EQUATION
`A N D SIMPLE SOLUTIONS
`
`5.1 Introduction
`
`113
`
`5.12 Decibel Scales
`
`130
`
`114
`
`5.2 The Equation of S t a t e
`5.3 T h e Equation
`of Continuity
`5.4 T h e Simple Force Equation:
`Euler's Equation
`1 17
`
`116
`
`5.5 T h e Linear Wave Equation
`
`1 19
`
`5.6 Speed of Sound i n Fluids
`
`120
`
`5.7 Harmonic Plane Waves
`
`121
`
`5.8 Energy Density
`
`124
`
`5.9 Acoustic Intensity
`5.10 Specific Acoustic
`Impedance
`126
`
`125
`
`*5.13 Cylindrical Waves
`*5.14 Rays a n d Waves
`
`133
`
`135
`
`(a) The Eikonal and Transport
`Equations
`135
`
`(b) The Equations
`fortheRaypath
`
`137
`
`(c) The One-Dimensional
`Gradient
`138
`
`(d) Phase and Intensity
`Considerations
`139
`
`*5.15 The Inhomogeneous
`Wave Equation
`140
`
`5.11 Spherical Waves
`
`127
`
`*5.16 The Point Source
`
`142
`
`CHAPTER 6
`REFLECTION A N D TRANSMISSION
`
`6.1 Changes i n Media
`
`149
`
`6.2 Transmission f r o m
`O n e Fluid t o Another:
`Normal Incidence
`150
`
`6.3 Transmission
`Through a Fluid Layer:
`Normal Incidence
`152
`
`6.4 Transmission f r o m
`O n e Fluid t o Another:
`Oblique Incidence
`155
`
`*6.5 Normal Specific Acoustic
`Impedance
`160
`
`www.SolutionManual.info
`
`*6.6 Reflection f r o m t h e Surface
`of a Solid
`160
`
`(a) Normal Incidence
`
`161
`
`(b) Oblique Incidence
`161
`*6.7 Transmission Through a Thin
`Partition: The Mass Law
`162
`
`6.8 Method of Images
`
`163
`
`(a) Rigid Boundary
`
`163
`
`(b) Pressure Release
`Boundary
`165
`
`(c) Extensions
`
`165
`
`CHAPTER 7
`RADIATION A N D RECEPTION OF ACOUSTIC WAVES
`
`7.1 Radiation f r o m a
`Pulsating Sphere
`
`171
`
`7.2 Acoustic Reciprocity
`a n d t h e Simple Source
`
`172
`
`7.3 T h e Continuous
`Line Source
`176
`
`7.4 Radiation f r o m a
`Plane Circular Piston
`
`179
`
`(a) Axial Response
`(b) Far Field
`
`181
`
`179
`
`7.5 Radiation Impedance
`
`184
`
`(a) The Circular Piston
`
`185
`
`(b) The Pulsating Sphere
`
`187
`
`7.6 Fundamental Properties
`of Transducers
`188
`
`(a) Directional Factor
`and Beam Pattern
`
`188
`
`(b) Beam Width
`
`188
`
`(c) Source Level
`
`188
`
`Page 10 of 43
`
`

`

`viii
`
`CONTENTS
`
`(d) Directivity
`
`189
`
`*7.8 The Line Array
`
`195
`
`(e) Directivity Index
`(f) Estimates
`of Radiation Patterns
`
`190
`
`1 9 1
`
`*7.9 T h e Product Theorem
`
`199
`
`*7.10 T h e Far Field Multipole
`Expansion
`199
`
`*7.7 Directional Factors
`of Reversible Transducers
`
`193
`
`*7.11 Beam Patterns a n d t h e Spatial
`Fourier Transform
`203
`
`CHAPTER 8
`ABSORPTION A N D ATTENUATION OF SOUND
`
`8.1 Introduction
`
`2 10
`
`8.2 Absorption
`from Viscosity
`
`2 1 1
`
`8.3 Complex Sound Speed
`a n d Absorption
`2 13
`
`8.4 Absorption f r o m
`Thermal Conduction
`
`215
`
`8.5 The Classical Absorption
`Coefficient
`2 17
`
`8.6 Molecular Thermal
`Relaxation
`2 18
`
`8.7 Absorption i n Liquids
`
`224
`
`*8.8 Viscous Losses
`a t a Rigid Wall
`
`228
`
`*8.9 Losses i n Wide Pipes
`
`2 3 0
`
`(a) Viscosity
`
`2 3 0
`
`(b) Thermal Conduction
`
`232
`
`(c) The Combined Absorption
`Coefficient
`233
`*8.10 Attenuation
`i n Suspensions
`
`234
`
`(a) Fogs
`235
`(b) Resonant Bubbles
`in Water
`238
`
`CHAPTER 9
`CAVITIES A N D WAVEGUIDES
`
`9.1 Introduction
`
`246
`
`9.2 Rectangular Cavity
`
`246
`
`*9.3 The Cylindrical Cavity
`
`2 4 9
`
`*9.4 The Spherical Cavity
`9.5 The Waveguide of Constant
`Cross Section
`252
`
`250
`
`*9.6 Sources a n d Transients i n
`Cavities a n d Waveguides
`
`256
`
`*9.7 The Layer
`a s a Waveguide
`
`259
`
`*9.8 An Isospeed Channel
`
`2 6 1
`
`*9.9 A W o - F l u i d Channel
`
`261
`
`CHAPTER 10
`PIPES, RESONATORS, A N D FILTERS
`
`10.1 Introduction
`
`272
`
`10.2 Resonance i n Pipes
`
`272
`
`10.3 Power Radiation
`from Open-Ended Pipes
`
`10.4 Standing Wave Patterns
`10.5 Absorption of Sound
`i n Pipes
`277
`
`275
`
`276
`
`10.6 Behavior of the Combined
`Driver-Pipe System
`280
`
`10.7 The Long Wavelength
`Limit
`283
`
`10.9 Acoustic Impedance
`(a) Lumped Acoustic
`Impedance
`287
`
`286
`
`(b) Distributed Acoustic
`Impedance
`287
`
`10.10 Reflection a n d
`Transmission of Waves
`in a Pipe
`288
`
`10.11 Acoustic Filters
`
`2 9 1
`
`(a) Low-Pass Filters
`
`2 9 1
`
`(b) High-Pass Filters
`
`293
`
`10.8 The Helmholtz Resonator
`
`284
`
`(c) Band-Stop Filters
`
`295
`
`Page 11 of 43
`
`

`

`CONTENTS
`
`www.elsolucionario.org
`
`CHAPTER 11
`NOISE, SIGNAL DETECTION, HEARING, A N D SPEECH
`
`11.1 Introduction
`
`302
`
`11.2 Noise, Spectrum Level,
`a n d Band Level
`302
`
`11.3 Combining Band Levels
`a n d Tones
`306
`
`*11.4 Detecting Signals
`i n Noise
`307
`
`*11.5 Detection Threshold
`
`3 10
`
`(a) Correlation Detection
`
`3 11
`
`(b) Energy Detection
`
`311
`
`*11.6 T h e Ear
`312
`11.7 S o m e Fundamental Properties
`of Hearing
`315
`
`(a) Thresholds
`
`316
`
`(b) Equal Loudness Level
`Contours
`318
`
`(c) Critical Bandwidth
`
`3 18
`
`(d) Masking
`
`320
`
`(el Beats, Combination Tones,
`and Aural Harmonics
`32 1
`
`(f) Consonance and the
`Restored Fundamental
`11.8 Loudness Level
`a n d Loudness
`
`324
`
`322
`
`11.9 Pitch a n d Frequency
`*11.10 The Voice
`327
`
`326
`
`CHAPTER 12
`ARCHITECTURAL ACOUSTICS
`
`12.1 Sound i n Enclosures
`
`333
`
`(a) The Direct Arrival
`
`343
`
`12.2 A Simple Model for t h e Growth
`of Sound i n a Room
`334
`
`12.3 Reverberation Time--
`Sabine
`336
`
`www.SolutionManual.info
`
`(b) Reverberation at 500 Hz
`
`343
`
`(c) Warmth
`
`345
`
`(d) Intimacy
`
`347
`
`12.4 Reverberation Time--
`Eyring a n d Norris
`338
`
`12.5 Sound Absorption
`Materials
`340
`
`12.6 Measurement of t h e Acoustic
`O u t p u t of Sound Sources
`in Live Rooms
`342
`12.7 Direct a n d
`Reverberant Sound
`
`342
`
`12.8 Acoustic Factors
`i n Architectural Design
`
`343
`
`(e) Diffusion, Blend,
`and Ensemble
`348
`*12.9 Standing Waves a n d Normal
`Modes i n Enclosures
`348
`
`(a) The Rectangular
`Enclosure
`349
`
`(b) Damped Normal Modes
`
`349
`
`(c) The Growth and Decay
`of Sound from a Source
`(dl Frequency Distribution of
`Enclosure Resonances
`353
`
`351
`
`CHAPTER 13
`ENVIRONMENTAL ACOUSTICS
`
`13.1 Introduction
`
`359
`
`13.2 Weighted Sound Levels
`13.3 Speech Interference
`
`362
`
`360
`
`13.7 Criteria for
`Community Noise
`
`369
`
`*13.8 Highway Noise
`
`371
`
`13.4 Privacy
`
`363
`
`*13.9 Aircraft Noise Rating
`
`373
`
`13.5 Noise Rating Curves
`13.6 The Statistical
`Description of
`Community Noise
`
`364
`
`365
`
`*13.10 Community Response
`t o Noise
`374
`
`13.11 Noise-Induced
`Hearing Loss
`
`375
`
`Page 12 of 43
`
`

`

`CONTENTS
`
`13.12 Noise a n d
`Architectural Design
`13.13 Specification a n d
`Measurement
`of Sound Isolation
`
`378
`
`379
`
`13.14 Recommended Isolation
`
`382
`
`13.15 Design of Partitions
`
`382
`
`(a) Single-Leaf Partitions
`
`383
`
`(b) Double-Leaf Partitions
`
`385
`
`(c) Doors and Windows
`
`387
`
`(d) Barriers
`
`387
`
`CHAPTER 14
`TRANSDUCTION
`
`14.1 Introduction
`
`390
`
`*14.7 Horn Loudspeakers
`
`414
`
`14.2 The Transducer as a n
`Electrical Network
`
`390
`
`14.8 Receivers
`
`416
`
`'
`
`(a) Microphone Directivity
`
`416
`
`(a) Reciprocal Transducers
`
`392
`
`(b) Antireciprocal
`Transducers
`
`393
`
`14.3 Canonical Equations for
`Two Simple Transducers
`
`394
`
`(a) The Electrostatic Transducer
`(Recivrocal)
`394
`
`1
`
`(b) The Moving-Coil Transducer
`(Antireciurocal) 396
`14.4 Transmitters
`
`398
`
`(a) Reciprocal Source
`
`399
`
`(b) Antireciprocal Source
`
`403
`
`(b) Microphone
`Sensitivities
`
`417
`
`(c) Reciprocal Receiver
`
`418
`
`(d) Antireciprocal
`Receiver
`418
`
`14.9 Condenser Microphone
`
`418
`
`14.10 Moving-Coil Electrodynamic
`Microphone
`420
`
`14.11 Pressure-Gradient
`Microphones
`423
`
`*14.12 Other Microphones
`
`425
`
`406
`
`425
`
`14.5 Moving-Coil Loudspeaker
`
`(a) The Carbon
`Microphone
`
`*14.6 Loudspeaker Cabinets
`
`411
`
`(b) The Piezoelectric
`
`(a) The Enclosed Cabinet
`
`411
`
`Microphone
`
`426
`
`(b) The Open Cabinet
`
`412
`
`(c) Fiber Optic Receivers
`
`427
`
`(c) Bass-Reflex Cabinet
`
`412
`
`*14.13 Calibration of Receivers
`
`428
`
`CHAPTER 15
`UNDERWATER ACOUSTICS
`
`15.1 Introduction
`
`435
`
`15.2 Speed of Sound
`in Seawater
`435
`
`15.3 Transmission Loss
`
`436
`
`15.4 Refraction
`
`438
`
`15.5 The Mixed Layer
`
`440
`
`15.6 The Deep Sound Channel a n d
`t h e Reliable Acoustic Path
`444
`
`15.9 Noise a n d Bandwidth
`Considerations
`450
`
`(a) Ambient Noise
`
`450
`
`(b) Self-Noise
`
`451
`
`(c) Doppler Shift
`
`453
`
`(d) Bandwidth
`Considerations
`
`454
`
`15.10 Passive Sonar
`
`455
`
`15.7 Surface Interference
`
`446
`
`(a) An Example
`
`456
`
`15.8 The Sonar Equations
`
`448
`
`15.11 Active Sonar
`
`456
`
`(a) Passive Sonar
`
`448
`
`(b) Active Sonar
`
`449
`
`(a) Target Strength
`
`457
`
`(b) Reverberation
`
`459
`
`Page 13 of 43
`
`

`

`CONTENTS
`
`(c) Detection Threshold
`for Reverberation-Limited
`Performance 463
`
`(dl An Example 464
`
`*15.12 Isospeed Shallow-Water
`Channel 465
`
`(a) Rigid Bottom 467
`
`(b) Slow Bottom 467
`(c) Fast Bottom 467
`
`*15.13 Transmission Loss Models
`for Normal-Mode
`Propagation 468
`
`(a) Rigid Bottom 470
`
`(b) FastBottom 470
`
`CHAPTER 16
`SELECTED NONLINEAR ACOUSTIC EFFECTS
`
`16.1 Introduction 478
`16.2 A Nonlinear Acoustic
`Wave Equation 478
`16.3 Two Descriptive
`Parameters 480
`
`(a) The Discontinuity
`Distance 481
`
`(b) The Goldberg Number
`16.4 Solution by Perturbation
`Expansion 483
`
`483
`
`16.5 Nonlinear
`Plane Waves 484
`
`(a) Traveling Waves
`in an Infinite
`Half-Space 484
`
`(b) Traveling Waves
`in a Pipe 485
`
`(c) Standing Waves
`i n a p i p e 487
`
`16.6 A Parametric Array 488
`
`www.SolutionManual.info
`CHAPTER 17
`SHOCK WAVES A N D EXPLOSIONS
`
`17.1 Shock Waves 494
`
`17.3 The Reference Explosion 501
`
`(a) The Rankine-Hugoniot
`Equations 495
`
`(b) Stagnation
`and Critical Flow 496
`
`(c) Normal Shock Relations
`
`(d) The Shock Adiabat 498
`
`17.2 T h e Blast Wave
`
`500
`
`(a) The Reference Chemical
`Explosion 501
`
`(b) The Reference Nuclear
`Explosion 502
`
`497
`
`17.4 The Scaling Laws 503
`
`17.5 Yield a n d t h e
`SurfaceEffect 504
`
`APPENDIXES
`
`509
`
`5 lo
`
`A1 Conversion Factors
`a n d Physical Constants 508
`A2 Complex Numbers
`A3 Circular a n d
`Hyperbolic Functions
`A4 Some Mathematical
`Functions
`5 10
`(a) Gamma Function
`(b) Bessel Functions,
`Modified Bessel Functions,
`and Struve Functions
`5 11
`
`510
`
`(c) Spherical Bessel
`Functions
`5 13
`
`(d) Legendre Functions
`
`513
`
`A5 Bessel Functions:
`Tables, Graphs, Zeros,
`a n d Extrema 514
`
`(a) Table: Bessel and
`Modified Bessel
`Functions of the
`First Kind of Orders
`O,l,and 2 514
`
`Page 14 of 43
`
`

`

`xii
`
`www.elsolucionario.org
`
`CONTENTS
`
`(b) Graphs: Bessel Functions
`of the First Kind of Orders
`0,1,2,and3
`516
`
`(c) Zeros: Bessel Functions
`of the First Kind,
`Jm(jmn)= 0
`516
`(d) Extrema: Bessel Functions
`of the First Kind,
`J f m ( j m n ) = 0
`516
`(e) Table: Spherical Bessel
`Functions of the First Kind
`of Orders O,1, and 2
`517
`
`(f) Graphs: Spherical Bessel
`Functions of the First Kind
`of Orders O,1, and 2
`518
`
`(g) Zeros: Spherical Bessel
`Functions of the First Kind,
`jm(gmn)= 0
`518
`(h) Extrema: Spherical Bessel
`Functions of the First Kind,
`j f m ( & n n ) = 0
`518
`
`A6 Table of Directivities
`a n d Impedance Functions
`for a Piston
`519
`
`A7 Vector Operators
`
`520
`
`(b) Cylindrical Coordinates
`
`520
`
`(c) Spherical Coordinates
`
`521
`
`A8 Gauss's Theorem
`a n d Green's Theorem
`
`5 2 1
`
`(a) Gauss's Theorem in Two-
`and Three-Dimensional
`Coordinate Systems
`5 2 1
`
`(b) Green's Theorem
`
`5 2 1
`
`A9 A Little Thermodynamics
`a n d t h e Perfect Gas
`522
`
`(a) Energy, Work, and the
`First Law
`522
`
`(b) Enthalpy, Entropy, and the
`Second Law
`523
`
`(c) The Perfect Gas
`524
`A10 Tables of Physical Properties
`of Matter
`526
`(a) Solids
`(b) Liquids
`
`527
`
`526
`
`(c) Gases
`
`528
`
`A1 1 Elasticity a n d Viscosity
`
`529
`
`(a) Solids
`
`(b) Fluids
`
`529
`
`531
`
`(a) Cartesian Coordinates
`
`520
`
`A12 The Greek Alphabet
`
`533
`
`ANSWERS TO ODD-NUMBERED PROBLEMS
`
`INDEX
`
`Page 15 of 43
`
`

`

`C h a p t e r 1
`
`FUNDAMENTALS
`OF VIBRATION
`
`1.1 INTRODUCTION
`
`Before beginning a discussion of acoustics, we should settle on a system of units.
`Acoustics encompasses such a wide range of scientific and engineering disciplines
`that the choice is not easy. A survey of the literature reveals a great lack of
`uniformity: writers use units common to their particular fields of interest. Most
`www.SolutionManual.info
`early work has been reported in the CGS (centimeter-gram-second) system, but
`considerable engineering work has been reported in a mixture of metric and
`English units. Work in electroacoustics and underwater acoustics has commonly
`been reported in the MKS (meter-kilogram-second) system. A codification of the
`MKS system, the SI (Le SystPme International &Unites), has been established as
`the standard. This is the system generally used in this book. CGS and SI units are
`equated and compared in Appendix Al.
`Throughout this text, "log" will represent logarithm to the base 10 and "ln" (the
`"natural logarithm") will represent logarithm to the base e.
`Acoustics as a science may be defined as the generation, transmission, and
`reception of energy as vibrational waves in matter. When the molecules of a fluid
`or solid are displaced from their normal configurations, an internal elastic restoring
`force arises. It is this elastic restoring force, coupled with the inertia of the system,
`that enables matter to participate in oscillatory vibrations and thereby generate
`and transmit acoustic waves. Examples include the tensile force produced when a
`spring is stretched, the increase in pressure produced when a fluid is compressed,
`and the restoring force produced when a point on a stretched wire is displaced
`transverse to its length.
`The most familiar acoustic phenomenon is that associated with the sensation of
`sound. For the average young person, a vibrational disturbance is interpreted as
`sound if its frequency lies in the interval from about 20 Hz to 20,000 Hz (1 Hz =
`I hertz = 1 cycle per second). However, in a broader sense acoustics also includes
`the ultrasonic frequencies above 20,000 Hz and the inpasonic frequencies below
`20 Hz. The natures of the vibrations associated with acoustics are many, including
`
`Page 16 of 43
`
`

`

`2
`
`CHAPTER 1 FUNDAMENTALS OF VIBRATION
`
`the simple sinusoidal vibrations produced by a tuning fork, the complex vibrations
`generated by a bowed violin string, and the nonperiodic motions associated with
`an explosion, to mention but a few. In studying vibrations it is advisable to begin
`with the simplest type, a one-dimensional sinusoidal vibration that has only a
`single frequency component (a pure tone).
`
`1.2 THE SIMPLE OSCILLATOR
`
`If a mass m, fastened to a spring and constrained to move parallel to the spring,
`is displaced slightly from its rest position and released, the mass will vibrate.
`Measurement shows that the displacement of the mass from its rest position is
`a sinusoidal function of time. Sinusoidal vibrations of this type are called simple
`harmonic vibrations. A large number of vibrators'used in acoustics can be modeled as
`simple oscillators. Loaded tuning forks and loudspeaker diaphragms, constructed
`so that at low frequencies their masses move as units, are but two examples.
`Even more complex vibrating systems have many of the characteristics of the
`simple systems and may often be modeled, to a first approximation, by simple
`oscillators.
`The only physical restrictions placed on the equations for the motion of a simple
`oscillator are that the restoring force be directly proportional to the displacement
`(Hooke's law), the mass be constant, and there be no losses to attenuate the
`motion. When these restrictions apply, the frequency of vibration is independent
`of amplitude and the motion is simple harmonic.
`A similar restriction applies to more complex types of vibration, such as the
`transmission of an acoustic wave through a fluid. If the acoustic pressures are so
`large that they no longer are proportional to the displacements of the particles of
`fluid, it becomes necessary to replace the normal acoustic equations with more
`general equations that are much more complicated. With sounds of ordinary
`intensity this is not necessary, for even the noise generated by a large crowd at a
`football game rarely causes the amplitude of motion of the air molecules to exceed
`one-tenth of a millimeter, which is within the limit given above. The amplitude of
`the shock wave generated by a large explosion is, however, well above this limit,
`and hence the normal acoustic equations are not applicable.
`Returning to the simple oscillator shown in Fig. 1.2.1, let us assume that the
`restoring force f in newtons (N) can be expressed by the equation
`
`Figure 1.2.1 Schematic representation of a simple
`oscillator consisting of a mass rn attached to one
`end of a spring of spring constant s. The other end
`of the spring is fixed.
`
`Page 17 of 43
`
`

`

`C h a p t e r 6
`
`REFLECTION AND
`TRANSMISSION
`
`6.1 CHANGES I N M E D I A
`
`When an acoustic wave traveling in one medium encounters the boundary of a
`second medium, reflected and transmitted waves are generated. Discussion of this
`phenomenon is greatly simplified if it is assumed that both the incident wave and
`the boundary between the media are planar and that all media are fluids. The
`www.SolutionManual.info
`complications that arise when one of the media is a solid will be left to Section
`6.6. However, it is worthwhile to note that for normal incidence many solids obey
`the same equations developed for fluids. The only modification needed is that the
`speed of sound in the solid must be the bulk speed of sound, based on both the bulk
`and shear moduli since, unlike the bar of Chapter 3, an extended solid is not free
`to change its transverse dimensions. See Appendix A l l . Values of the bulk speeds
`of sound in some solids are listed in Appendix A10.
`The ratios of the pressure amplitudes and intensities of the reflected and
`transmitted waves to those of the incident wave depend on the characte