Springer Handbookof Acoustics

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123

HandbookSpringerof Acoustics

Thomas D. Rossing (Ed.)

With CD-ROM, 962 Figures and 91 Tables

Editor:

Thomas D. RossingStanford UniversityCenter for Computer Research in Music and AcousticsStanford, CA 94305, USA

Editorial Board:

Manfred R. Schroeder, University of Göttingen, GermanyWilliam M. Hartmann, Michigan State University, USANeville H. Fletcher, Australian National University, AustraliaFloyd Dunn, University of Illinois, USAD. Murray Campbell, The University of Edinburgh, UK

Library of Congress Control Number: 2006927050

ISBN: 978-0-387-30446-5 e-ISBN: 0-387-30425-0Printed on acid free paper

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V

Foreword

Prof. Dr. M. R. SchroederUniversity ProfessorSpeach and Acoustics LaboratoryUniversity of Göttingen,Germany

The present handbook covers a very wide field. Its 28 chapters range from the historyof acoustics to sound propagation in the atmosphere; from nonlinear and underwa-ter acoustics to thermoacoustics and concert hall acoustics. Also covered are musicalacoustics, including computer and electronic music; speech and singing; animal (in-cluding whales) communication as well as bioacoustics in general, psychoacousticsand medical acoustics. In addition, there are chapters on structural acoustics, vibrationand noise, including optical methods for their measurement; microphones, their cali-bration, and microphone and hydrophone arrays; acoustic holography; model analysisand much else needed by the professional engineer and scientist.

Among the authors we find many illustrious names: Yoichi Ando, Mack Breazeale,Babrina Dunmire, Neville Fletcher, Anders Gade, William Hartmann, William Kuper-man, Werner Lauterborn, George Maling, Brian Moore, Allan Pierce, Thomas Rossing,Johan Sundberg, Eric Young, and many more. They hail from countries around theworld: Australia, Canada, Denmark, France, Germany, Japan, Korea, Sweden, theUnited Kingdom, and the USA. There is no doubt that this handbook will fill manyneeds, nay be irreplaceable in the art of exercising today’s many interdisciplinary tasksdevolving on acoustics. No reader could wish for a wider and more expert coverage.I wish the present tome the wide acceptance and success it surely deserves.

Göttingen, March 2007 Manfred R. Schroeder

VII

Preface

Prof. em. T. D. RossingNorthern Illinois UniversityPresently visiting Professorof Music at Stanford University

“A handbook,” according to the dictionary, “is a book capable of being convenientlycarried as a ready reference.” Springer has created the Springer Handbook series onimportant scientific and technical subjects, and we feel fortunate that they have includedacoustics in this category.

Acoustics, the science of sound, is a rather broad subject to be covered in a singlehandbook. It embodies many different academic disciplines, such as physics, mechan-ical and electrical engineering, mathematics, speech and hearing sciences, music, andarchitecture. There are many technical areas in acoustics; the Acoustical Society ofAmerica, for example, includes 14 technical committees representing different areasof acoustics. It is impossible to cover all of these areas in a single handbook. We havetried to include as many as possible of the “hot” topics in this interdisciplinary field, in-cluding basic science and technological applications. We apologize to the reader whosefavorite topics are not included.

We have grouped the 28 chapters in the book into eight parts: Propagation ofSound; Physical and Nonlinear Acoustics; Architectural Acoustics; Hearing and SignalProcessing; Music, Speech, and Electroacoustics; Biological and Medical Acoustics;Structural Acoustics and Noise; and Engineering Acoustics. The chapters are of varyinglength. They also reflect the individual writing styles of the various authors, all of whomare authorities in their fields. Although an attempt was made to keep the mathematicallevel of the chapters as even as possible, readers will note that some chapters are moremathematical than others; this is unavoidable and in fact lends some degree of richnessto the book.

We are indebted to many persons, especially Werner Skolaut, the manager of theSpringer Handbooks, and to the editorial board, consisting of Neville Fletcher, FloydDunn, William Hartmann, and Murray Campbell, and for their advice. Each chapterwas reviewed by two authoritative reviewers, and we are grateful to them for their ser-vices. But most of all we thank the authors, all of whom are busy people but devotedmuch time to carefully preparing their chapters.

Stanford, April 2007 Thomas D. Rossing

IX

List of Authors

Iskander AkhatovNorth Dakota State UniversityCenter for Nanoscale Science and Engineering,Department of Mechanical Engineering111 Dolve HallFargo, ND 58105-5285, USAe-mail: iskander.akhatov@ndsu.edu

Yoichi Ando3917-680 Takachiho899-6603 Makizono, Kirishima, Japane-mail: andoy@cameo.plala.or.jp

Keith AttenboroughThe University of HullDepartment of EngineeringCottingham RoadHull, HU6 7RX, UKe-mail: k.attenborough@hull.ac.uk

Whitlow W. L. AuHawaii Institute of Marine BiologyP.O. Box 1106Kailua, HI 96734, USAe-mail: wau@hawaii.edu

Kirk W. BeachUniversity of WashingtonDepartment of SurgerySeattle, WA 98195, USAe-mail: kwbeach@u.washington.edu

Mack A. BreazealeUniversity of MississippiNational Center for Physical Acoustics027 NCPA Bldg.University, MS 38677, USAe-mail: breazeal@olemiss.edu

Antoine ChaigneUnité de Mécanique (UME)Ecole Nationale Supérieure de TechniquesAvancées (ENSTA)Chemin de la Hunière91761 Palaiseau, Francee-mail: antoine.chaigne@ensta.fr

Perry R. CookPrinceton UniversityDepartment of Computer Science35 Olden StreetPrinceton, NJ 08540, USAe-mail: prc@cs.princeton.edu

James CowanResource Systems Group Inc.White River Junction, VT 85001, USAe-mail: jcowan@rsginc.com

Mark F. DavisDolby Laboratories100 Potrero Ave,San Francisco, CA 94103, USAe-mail: mfd@dolby.com

Barbrina DunmireUniversity of WashingtonApplied Physics Laboratory1013 NE 40th Str.Seattle, WA 98105, USAe-mail: mrbean@u.washington.edu

Neville H. FletcherAustralian National UniversityResearch School of Physical Sciences andEngineeringCanberra, ACT 0200, Australiae-mail: neville.fletcher@anu.edu.au

Anders Christian GadeTechnical University of DenmarkAcoustic Technology, Oersted.DTUBuilding 3522800 Lyngby, Denmarke-mail: acg@oersted.dtu.dk,anders.gade@get2net.dk

Colin GoughUniversity of BirminghamSchool of Physics and AstronomyBirmingham, B15 2TT, UKe-mail: c.gough@bham.ac.uk

X List of Authors

William M. HartmannMichigan State University1226 BPS BuildingEast Lansing, MI 48824, USAe-mail: hartmann@pa.msu.edu

Finn JacobsenØrsted DTU, Technical University of DenmarkAcoustic TechnologyØrsteds Plads, Building 3522800 Lyngby, Denmarke-mail: fja@oersted.dtu.dk

Yang-Hann KimKorea Advanced Institute of Scienceand Technology (KAIST)Department of Mechanical EngineeringCenter for Noise and Vibration Control (NOVIC)Acoustics and Vibration Laboratory373-1 Kusong-dong, Yusong-guDaejeon, 305-701, Koreae-mail: yanghannkim@kaist.ac.kr

William A. KupermanUniversity of California at San DiegoScripps Institution of Oceanography9500 Gilman DriveLa Jolla, CA 92093-0701, USAe-mail: wkuperman@ucsd.edu

Thomas KurzUniversität GöttingenFriedrich-Hund-Platz 137077 Göttingen, Germanye-mail: t.kurz@dpi.physik.uni-goettingen.de

Marc O. LammersHawaii Institute of Marine BiologyP.O. Box 1106Kailua, HI 96734, USAe-mail: lammers@hawaii.edu

Werner LauterbornUniversität GöttingenDrittes Physikalisches InstitutFriedrich-Hund-Platz 137077 Göttingen, Germanye-mail:w.lauterborn@dpi.physik.uni-goettingen.de

Björn LindblomStockholm UniversityDepartment of Linguistics10691 Stockholm, Swedene-mail: lindblom@ling.su.se,blindblom@mail.utexas.edu

George C. Maling, Jr.Institute of Noise Control Engineering of the USA60 High Head RoadHarpswell, ME 04079, USAe-mail: maling@alum.mit.edu

Michael McPhersonThe University of MississippiDepartment of Physics and Astronomy123 Lewis HallP. O. Box 1848University, MS 38677, USAe-mail: mcph@phy.olemiss.edu

Nils-Erik MolinLuleå University of TechnologyExperimental MechanicsSE-971 87 Luleå, Swedene-mail: nem@ltu.se

Brian C. J. MooreUniversity of CambridgeDepartment of Experimental PsychologyDowning StreetCambridge, CB2 3EB, UKe-mail: bcjm@cam.ac.uk

Alan D. PierceBoston UniversityCollege of EngineeringBoston, MA , USAe-mail: adp@bu.edu

Thomas D. RossingStanford UniversityCenter for Computer Research in Music andAcoustics (CCRMA)Department of MusicStanford, CA 94305, USAe-mail: rossing@ccrma.stanford.edu

List of Authors XI

Philippe RouxUniversité Joseph FourierLaboratoire de Geophysique Interne etTectonophysique38041 Grenoble, Francee-mail: philippe.roux@obs.ujf-grenoble.fr

Johan SundbergKTH–Royal Institute of TechnologyDepartment of Speech, Music, and HearingSE-10044 Stockholm, Swedene-mail: pjohan@speech.kth.se

Gregory W. SwiftLos Alamos National LaboratoryCondensed Matter and Thermal Physics GroupLos Alamos, NM 87545, USAe-mail: swift@lanl.gov

George S. K. WongInstitute for National Measurement Standards(INMS)National Research Council Canada (NRC)1200 Montreal RoadOttawa, ON K1A 0R6, Canadae-mail: George.Wong@nrc-cnrc.gc.ca

Eric D. YoungJohns Hopkins UniversityBaltimore, MD 21205, USAe-mail: eyoung@jhu.edu

XIII

Contents

List of Abbreviations ................................................................................. XXI

1 Introduction to AcousticsThomas D. Rossing................................................................................... 11.1 Acoustics: The Science of Sound ..................................................... 11.2 Sounds We Hear ............................................................................ 11.3 Sounds We Cannot Hear: Ultrasound and Infrasound ...................... 21.4 Sounds We Would Rather Not Hear: Environmental Noise Control..... 21.5 Aesthetic Sound: Music .................................................................. 31.6 Sound of the Human Voice: Speech and Singing ............................. 31.7 How We Hear: Physiological and Psychological Acoustics ................. 41.8 Architectural Acoustics ................................................................... 41.9 Harnessing Sound: Physical and Engineering Acoustics ................... 51.10 Medical Acoustics .......................................................................... 51.11 Sounds of the Sea ......................................................................... 6References .............................................................................................. 6

Part A Propagation of Sound

2 A Brief History of AcousticsThomas D. Rossing................................................................................... 92.1 Acoustics in Ancient Times ............................................................. 92.2 Early Experiments on Vibrating Strings, Membranes and Plates ....... 102.3 Speed of Sound in Air .................................................................... 102.4 Speed of Sound in Liquids and Solids ............................................. 112.5 Determining Frequency ................................................................. 112.6 Acoustics in the 19th Century ......................................................... 122.7 The 20th Century ........................................................................... 152.8 Conclusion .................................................................................... 23References .............................................................................................. 23

3 Basic Linear AcousticsAlan D. Pierce .......................................................................................... 253.1 Introduction ................................................................................. 273.2 Equations of Continuum Mechanics ................................................ 283.3 Equations of Linear Acoustics ......................................................... 353.4 Variational Formulations ............................................................... 403.5 Waves of Constant Frequency ......................................................... 453.6 Plane Waves.................................................................................. 47

XIV Contents

3.7 Attenuation of Sound .................................................................... 493.8 Acoustic Intensity and Power ......................................................... 583.9 Impedance ................................................................................... 603.10 Reflection and Transmission .......................................................... 613.11 Spherical Waves ............................................................................ 653.12 Cylindrical Waves .......................................................................... 753.13 Simple Sources of Sound ................................................................ 823.14 Integral Equations in Acoustics ...................................................... 873.15 Waveguides, Ducts, and Resonators ............................................... 893.16 Ray Acoustics ................................................................................ 943.17 Diffraction .................................................................................... 983.18 Parabolic Equation Methods .......................................................... 107References .............................................................................................. 108

4 Sound Propagation in the AtmosphereKeith Attenborough ................................................................................. 1134.1 A Short History of Outdoor Acoustics ............................................... 1134.2 Applications of Outdoor Acoustics ................................................... 1144.3 Spreading Losses ........................................................................... 1154.4 Atmospheric Absorption................................................................. 1164.5 Diffraction and Barriers ................................................................. 1164.6 Ground Effects .............................................................................. 1204.7 Attenuation Through Trees and Foliage .......................................... 1294.8 Wind and Temperature Gradient Effects on Outdoor Sound ............. 1314.9 Concluding Remarks ...................................................................... 142References .............................................................................................. 143

5 Underwater AcousticsWilliam A. Kuperman, Philippe Roux ........................................................ 1495.1 Ocean Acoustic Environment .......................................................... 1515.2 Physical Mechanisms ..................................................................... 1555.3 SONAR and the SONAR Equation ...................................................... 1655.4 Sound Propagation Models ............................................................ 1675.5 Quantitative Description of Propagation ......................................... 1775.6 SONAR Array Processing .................................................................. 1795.7 Active SONAR Processing ................................................................. 1855.8 Acoustics and Marine Animals ........................................................ 1955.A Appendix: Units ............................................................................ 201References .............................................................................................. 201

Part B Physical and Nonlinear Acoustics

6 Physical AcousticsMack A. Breazeale, Michael McPherson ..................................................... 2076.1 Theoretical Overview ..................................................................... 2096.2 Applications of Physical Acoustics ................................................... 219

Contents XV

6.3 Apparatus ..................................................................................... 2266.4 Surface Acoustic Waves .................................................................. 2316.5 Nonlinear Acoustics ....................................................................... 234References .............................................................................................. 237

7 ThermoacousticsGregory W. Swift ...................................................................................... 2397.1 History .......................................................................................... 2397.2 Shared Concepts ............................................................................ 2407.3 Engines......................................................................................... 2447.4 Dissipation.................................................................................... 2497.5 Refrigeration ................................................................................. 2507.6 Mixture Separation ........................................................................ 253References .............................................................................................. 254

8 Nonlinear Acoustics in FluidsWerner Lauterborn, Thomas Kurz, Iskander Akhatov .................................. 2578.1 Origin of Nonlinearity .................................................................... 2588.2 Equation of State .......................................................................... 2598.3 The Nonlinearity Parameter B/A ..................................................... 2608.4 The Coefficient of Nonlinearity β .................................................... 2628.5 Simple Nonlinear Waves ................................................................ 2638.6 Lossless Finite-Amplitude Acoustic Waves ....................................... 2648.7 Thermoviscous Finite-Amplitude Acoustic Waves............................. 2688.8 Shock Waves ................................................................................. 2718.9 Interaction of Nonlinear Waves ...................................................... 2738.10 Bubbly Liquids .............................................................................. 2758.11 Sonoluminescence ........................................................................ 2868.12 Acoustic Chaos .............................................................................. 289References .............................................................................................. 293

Part C Architectural Acoustics

9 Acoustics in Halls for Speech and MusicAnders Christian Gade .............................................................................. 3019.1 Room Acoustic Concepts ................................................................. 3029.2 Subjective Room Acoustics ............................................................. 3039.3 Subjective and Objective Room Acoustic Parameters ........................ 3069.4 Measurement of Objective Parameters ............................................ 3149.5 Prediction of Room Acoustic Parameters ......................................... 3169.6 Geometric Design Considerations ................................................... 3239.7 Room Acoustic Design of Auditoria for Specific Purposes .................. 3349.8 Sound Systems for Auditoria .......................................................... 346References .............................................................................................. 349

XVI Contents

10 Concert Hall Acoustics Based on Subjective Preference TheoryYoichi Ando ............................................................................................. 35110.1 Theory of Subjective Preference for the Sound Field ........................ 35310.2 Design Studies .............................................................................. 36110.3 Individual Preferences of a Listener and a Performer ...................... 37010.4 Acoustical Measurements of the Sound Fields in Rooms .................. 377References .............................................................................................. 384

11 Building AcousticsJames Cowan........................................................................................... 38711.1 Room Acoustics ............................................................................. 38711.2 General Noise Reduction Methods .................................................. 40011.3 Noise Ratings for Steady Background Sound Levels.......................... 40311.4 Noise Sources in Buildings ............................................................. 40511.5 Noise Control Methods for Building Systems .................................... 40711.6 Acoustical Privacy in Buildings ....................................................... 41911.7 Relevant Standards ....................................................................... 424References .............................................................................................. 425

Part D Hearing and Signal Processing

12 Physiological AcousticsEric D. Young ........................................................................................... 42912.1 The External and Middle Ear .......................................................... 42912.2 Cochlea ......................................................................................... 43412.3 Auditory Nerve and Central Nervous System .................................... 44912.4 Summary ...................................................................................... 452References .............................................................................................. 453

13 PsychoacousticsBrian C. J. Moore ...................................................................................... 45913.1 Absolute Thresholds ...................................................................... 46013.2 Frequency Selectivity and Masking ................................................. 46113.3 Loudness ...................................................................................... 46813.4 Temporal Processing in the Auditory System ................................... 47313.5 Pitch Perception ............................................................................ 47713.6 Timbre Perception ......................................................................... 48313.7 The Localization of Sounds ............................................................. 48413.8 Auditory Scene Analysis ................................................................. 48513.9 Further Reading and Supplementary Materials ............................... 494References .............................................................................................. 495

14 Acoustic Signal ProcessingWilliam M. Hartmann .............................................................................. 50314.1 Definitions .................................................................................... 50414.2 Fourier Series ................................................................................ 505

Contents XVII

14.3 Fourier Transform .......................................................................... 50714.4 Power, Energy, and Power Spectrum .............................................. 51014.5 Statistics ....................................................................................... 51114.6 Hilbert Transform and the Envelope ............................................... 51414.7 Filters ........................................................................................... 51514.8 The Cepstrum ................................................................................ 51714.9 Noise ............................................................................................ 51814.10 Sampled data ............................................................................... 52014.11 Discrete Fourier Transform ............................................................. 52214.12 The z-Transform............................................................................ 52414.13 Maximum Length Sequences .......................................................... 52614.14 Information Theory ....................................................................... 528References .............................................................................................. 530

Part E Music, Speech, Electroacoustics

15 Musical AcousticsColin Gough ............................................................................................ 53315.1 Vibrational Modes of Instruments .................................................. 53515.2 Stringed Instruments ..................................................................... 55415.3 Wind Instruments ......................................................................... 60115.4 Percussion Instruments ................................................................. 641References .............................................................................................. 661

16 The Human Voice in Speech and SingingBjörn Lindblom, Johan Sundberg ............................................................. 66916.1 Breathing ..................................................................................... 66916.2 The Glottal Sound Source ............................................................... 67616.3 The Vocal Tract Filter ...................................................................... 68216.4 Articulatory Processes, Vowels and Consonants ............................... 68716.5 The Syllable................................................................................... 69516.6 Rhythm and Timing ....................................................................... 69916.7 Prosody and Speech Dynamics ....................................................... 70116.8 Control of Sound in Speech and Singing ......................................... 70316.9 The Expressive Power of the Human Voice ...................................... 706References .............................................................................................. 706

17 Computer MusicPerry R. Cook ........................................................................................... 71317.1 Computer Audio Basics .................................................................. 71417.2 Pulse Code Modulation Synthesis ................................................... 71717.3 Additive (Fourier, Sinusoidal) Synthesis .......................................... 71917.4 Modal (Damped Sinusoidal) Synthesis ............................................ 72217.5 Subtractive (Source-Filter) Synthesis............................................... 72417.6 Frequency Modulation (FM) Synthesis ............................................. 72717.7 FOFs, Wavelets, and Grains ............................................................ 728

XVIII Contents

17.8 Physical Modeling (The Wave Equation) .......................................... 73017.9 Music Description and Control ........................................................ 73517.10 Composition .................................................................................. 73717.11 Controllers and Performance Systems ............................................. 73717.12 Music Understanding and Modeling by Computer ........................... 73817.13 Conclusions, and the Future .......................................................... 740References .............................................................................................. 740

18 Audio and ElectroacousticsMark F. Davis........................................................................................... 74318.1 Historical Review ........................................................................... 74418.2 The Psychoacoustics of Audio and Electroacoustics .......................... 74718.3 Audio Specifications ...................................................................... 75118.4 Audio Components ........................................................................ 75718.5 Digital Audio ................................................................................. 76818.6 Complete Audio Systems ................................................................ 77518.7 Appraisal and Speculation ............................................................. 778References .............................................................................................. 778

Part F Biological and Medical Acoustics

19 Animal BioacousticsNeville H. Fletcher .................................................................................... 78519.1 Optimized Communication ............................................................. 78519.2 Hearing and Sound Production ...................................................... 78719.3 Vibrational Communication ........................................................... 78819.4 Insects .......................................................................................... 78819.5 Land Vertebrates ........................................................................... 79019.6 Birds............................................................................................. 79519.7 Bats .............................................................................................. 79619.8 Aquatic Animals ............................................................................ 79719.9 Generalities .................................................................................. 79919.10 Quantitative System Analysis.......................................................... 799References .............................................................................................. 802

20 Cetacean AcousticsWhitlow W. L. Au, Marc O. Lammers .......................................................... 80520.1 Hearing in Cetaceans ..................................................................... 80620.2 Echolocation Signals ...................................................................... 81320.3 Odontocete Acoustic Communication .............................................. 82120.4 Acoustic Signals of Mysticetes ......................................................... 82720.5 Discussion ..................................................................................... 830References .............................................................................................. 831

21 Medical AcousticsKirk W. Beach, Barbrina Dunmire ............................................................. 83921.1 Introduction to Medical Acoustics ................................................... 841

Contents XIX

21.2 Medical Diagnosis; Physical Examination ........................................ 84221.3 Basic Physics of Ultrasound Propagation in Tissue ........................... 84821.4 Methods of Medical Ultrasound Examination .................................. 85721.5 Medical Contrast Agents ................................................................. 88221.6 Ultrasound Hyperthermia in Physical Therapy ................................. 88921.7 High-Intensity Focused Ultrasound (HIFU) in Surgery ....................... 89021.8 Lithotripsy of Kidney Stones ........................................................... 89121.9 Thrombolysis ................................................................................. 89221.10 Lower-Frequency Therapies ........................................................... 89221.11 Ultrasound Safety .......................................................................... 892References .............................................................................................. 895

Part G Structural Acoustics and Noise

22 Structural Acoustics and VibrationsAntoine Chaigne ...................................................................................... 90122.1 Dynamics of the Linear Single-Degree-of-Freedom (1-DOF)

Oscillator ...................................................................................... 90322.2 Discrete Systems ............................................................................ 90722.3 Strings and Membranes ................................................................. 91322.4 Bars, Plates and Shells................................................................... 92022.5 Structural–Acoustic Coupling .......................................................... 92622.6 Damping ....................................................................................... 94022.7 Nonlinear Vibrations ..................................................................... 94722.8 Conclusion. Advanced Topics .......................................................... 957References .............................................................................................. 958

23 NoiseGeorge C. Maling, Jr................................................................................. 96123.1 Instruments for Noise Measurements ............................................. 96523.2 Noise Sources ................................................................................ 97023.3 Propagation Paths ......................................................................... 99123.4 Noise and the Receiver .................................................................. 99923.5 Regulations and Policy for Noise Control ......................................... 100623.6 Other Information Resources .......................................................... 1010References .............................................................................................. 1010

Part H Engineering Acoustics

24 Microphones and Their CalibrationGeorge S. K. Wong.................................................................................... 102124.1 Historic References on Condenser Microphones and Calibration ....... 102424.2 Theory .......................................................................................... 102424.3 Reciprocity Pressure Calibration ..................................................... 102624.4 Corrections .................................................................................... 1029

XX Contents

24.5 Free-Field Microphone Calibration ................................................. 103924.6 Comparison Methods for Microphone Calibration ............................ 103924.7 Frequency Response Measurement with Electrostatic Actuators ....... 104324.8 Overall View on Microphone Calibration ......................................... 104324.A Acoustic Transfer Impedance Evaluation ......................................... 104524.B Physical Properties of Air ............................................................... 1045References .............................................................................................. 1048

25 Sound IntensityFinn Jacobsen.......................................................................................... 105325.1 Conservation of Sound Energy ........................................................ 105425.2 Active and Reactive Sound Fields ................................................... 105525.3 Measurement of Sound Intensity.................................................... 105825.4 Applications of Sound Intensity ...................................................... 1068References .............................................................................................. 1072

26 Acoustic HolographyYang-Hann Kim ...................................................................................... 107726.1 The Methodology of Acoustic Source Identification .......................... 107726.2 Acoustic Holography: Measurement, Prediction and Analysis ........... 107926.3 Summary ...................................................................................... 109226.A Mathematical Derivations of Three Acoustic Holography Methods

and Their Discrete Forms................................................................ 1092References .............................................................................................. 1095

27 Optical Methods for Acoustics and Vibration MeasurementsNils-Erik Molin ........................................................................................ 110127.1 Introduction ................................................................................. 110127.2 Measurement Principles and Some Applications.............................. 110527.3 Summary ...................................................................................... 1122References .............................................................................................. 1123

28 Modal AnalysisThomas D. Rossing................................................................................... 112728.1 Modes of Vibration ........................................................................ 112728.2 Experimental Modal Testing ........................................................... 112828.3 Mathematical Modal Analysis ......................................................... 113328.4 Sound-Field Analysis ..................................................................... 113628.5 Holographic Modal Analysis ........................................................... 1137References .............................................................................................. 1138

Acknowledgements ................................................................................... 1139About the Authors ..................................................................................... 1141Detailed Contents ...................................................................................... 1147Subject Index ............................................................................................. 1167

XXI

List of Abbreviations

A

ABR auditory brainstem responsesAC articulation classACF autocorrelation functionADC analog-to-digital converterADCP acoustic Doppler current profilerADP ammonium dihydrogen phosphateAM amplitude modulatedAMD air moving deviceAN auditory nerveANSI American National Standards InstituteAR assisted resonanceASW apparent source widthAUV automated underwater vehicle

B

BB bite blockBEM boundary-element methodBER bit error rateBF best frequencyBR bass ratio

C

CAATI computed angle-of-arrival transientimaging

CAC ceiling attenuation classCCD charge-coupled deviceCDF cumulative distribution functionCMU concrete masonry unitCN cochlear nucleusCND cumulative normal distributionCSDM cross-spectral-density matrix

D

DAC digital-to-analog converterDL difference limenDOF degree of freedomDRS directed reflection sequenceDSL deep scattering layerDSP digital speckle photographyDSP digital signal processingDSPI digital speckle-pattern interferometry

E

EARP equal-amplitude random-phaseEDT early decay time

EDV end diastolic velocityEEG electroencephalographyEOF empirical orthogonal functionEOH electro-optic holographyERB equivalent rectangular bandwidthESPI electronic speckle-pattern interferometry

F

FCC Federal Communications CommissionFEA finite-element analysisFEM finite-element methodFERC Federal Energy Regulatory CommissionFFP fast field programFFT fast Fourier transformFIR finite impulse responseFM frequency modulatedFMDL frequency modulation detection limenFOM figure of meritFRF frequency response functionFSK frequency shift keying

G

GA genetic algorithm

H

HVAC heating, ventilating and air conditioning

I

IACC interaural cross-correlation coefficientIACF interaural cross-correlation functionIAD interaural amplitude differenceICAO International Civil Aircraft OrganizationIF intermediate frequencyIFFT inverse fast Fourier transformIHC inner hair cellsIIR infinite impulse responseIM intermodulationIRF impulse response functionISI intersymbol interferenceITD interaural time differenceITDG initial time delay gap

J

JND just noticeable difference

XXII List of Abbreviations

K

KDP potassium dihydrogen phosphate

L

LDA laser Doppler anemometryLDV laser Doppler vibrometryLEF lateral energy fractionLEV listener envelopmentLL listening levelLOC lateral olivocochlear systemLP long-play vinyl recordLTAS long-term-average spectra

M

MAA minimum audible angleMAF minimum audible fieldMAP minimum audible pressureMCR multichannel reverberationMDOF multiple degree of freedomMEG magnetoencephalogramMEMS microelectromechanical systemMFDR maximum flow declination rateMFP matched field processingMIMO multiple-input multiple-outputMLM maximum-likelihood methodMLS maximum length sequenceMOC medial olivocochlear systemMRA main response axisMRI magnetic resonance imagingMTF modulation transfer functionMTS multichannel television soundMV minimum variance

N

NDT nondestructive testingNMI National Metrology InstituteNRC noise reduction coefficient

O

OAE otoacoustic emissionODS operating deflexion shapeOHC outer hair cellsOITC outdoor–indoor transmission classOR or operationOSHA Occupational Safety and Health

Administration

P

PC phase conjugationPCM pulse code modulation

PD probability of detectionPDF probability density functionPE parabolic equationPFA probability of false alarmPIV particle image velocimetryPL propagation lossPLIF planar laser-induced fluorescentPM phase modulationPMF probability mass functionPS phase steppingPS peak systolicPSD power spectral densityPSK phase shift keyingPTC psychophysical tuning curvePVDF polyvinylidene fluoridePZT lead zirconate titanate

Q

QAM quadrature amplitude modulation

R

RASTI rapid speech transmission indexREL resting expiratory levelRF radio frequencyRIAA Recording Industry Association of

AmericaRMS root-mean-squareROC receiving operating characteristicRUS resonant ultrasound spectroscopy

S

s.c. supporting cellsS/N signal-to-noiseSAA sound absorption averageSAC spatial audio codingSAW surface acoustic waveSBSL single-bubble sonoluminescenceSDOF single degree of freedomSE signal excessSEA statistical energy analysisSG spiral ganglionSI speckle interferometrySIL speech interference levelSIL sound intensity levelSISO single-input single-outputSL sensation levelSM scala mediaSNR signal-to-noise ratioSOC superior olivary complexSP speckle photographySPL sound pressure levelSR spontaneous discharge rateST scala tympani

List of Abbreviations XXIII

STC sound transmission classSTI speech transmission indexSV scala vestibuliSVR slow vertex response

T

TDAC time-domain alias cancellationTDGF time-domain Green’s functionTHD total harmonic distortionTL transmission lossTLC total lung capacityTMTF temporal modulation transfer functionTNM traffic noise modelTR treble ratioTR time reversalTTS temporary threshold shiftTVG time-varied gain

U

UMM unit modal mass

V

VBR variable bitrateVC vital capacity

W

WS working standard

X

XOR exclusive or

1

Introduction t1. Introduction to Acoustics

This brief introduction may help to persuadethe reader that acoustics covers a wide range ofinteresting topics. It is impossible to cover allthese topics in a single handbook, but we haveattempted to include a sampling of hot topicsthat represent current acoustical research, bothfundamental and applied.

Acoustics is the science of sound. It dealswith the production of sound, the propagationof sound from the source to the receiver, andthe detection and perception of sound. The wordsound is often used to describe two differentthings: an auditory sensation in the ear, andthe disturbance in a medium that can cause thissensation. By making this distinction, the age-oldquestion “If a tree falls in a forest and no one isthere to hear it, does it make a sound?” can beanswered.

1.1 Acoustics: The Science of Sound ............ 1

1.2 Sounds We Hear .................................. 1

1.3 Sounds We Cannot Hear:Ultrasound and Infrasound .................. 2

1.4 Sounds We Would Rather Not Hear:Environmental Noise Control ................ 2

1.5 Aesthetic Sound: Music ........................ 3

1.6 Sound of the Human Voice:Speech and Singing ............................. 3

1.7 How We Hear: Physiologicaland Psychological Acoustics .................. 4

1.8 Architectural Acoustics ......................... 4

1.9 Harnessing Sound:Physical and Engineering Acoustics ....... 5

1.10 Medical Acoustics................................. 5

1.11 Sounds of the Sea ................................ 6

References .................................................. 6

1.1 Acoustics: The Science of Sound

Acoustics has become a broad interdisciplinary fieldencompassing the academic disciplines of physics, en-gineering, psychology, speech, audiology, music, archi-tecture, physiology, neuroscience, and others. Amongthe branches of acoustics are architectural acoustics,physical acoustics, musical acoustics, psychoacoustics,electroacoustics, noise control, shock and vibration, un-derwater acoustics, speech, physiological acoustics, etc.

Sound can be produced by a number of differentprocesses, which include the following.

Vibrating bodies: when a drumhead or a noisy ma-chine vibrates, it displaces air and causes the local airpressure to fluctuate.

Changing airflow: when we speak or sing, our vocalfolds open and close to let through puffs of air. In a siren,holes on a rapidly rotating plate alternately pass andblock air, resulting in a loud sound.

Time-dependent heat sources: an electrical sparkproduces a crackle; an explosion produces a bangdue to the expansion of air caused by rapid heat-ing. Thunder results from rapid heating by a bolt oflightning.

Supersonic flow: shock waves result when a super-sonic airplane or a speeding bullet forces air to flowfaster than the speed of sound.

1.2 Sounds We Hear

The range of sound intensity and the range of fre-quency to which the human auditory system respondsis quite remarkable. The intensity ratio between the

sounds that bring pain to our ears and the weakestsounds we can hear is more than 1012. The frequencyratio between the highest and lowest frequencies we

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can hear is nearly 103, or more than nine octaves (eachoctave representing a doubling of frequency). Humanvision is also quite remarkable, but the frequency rangedoes not begin to compare to that of human hearing.The frequency range of vision is a little less than oneoctave (about 4 × 1014 –7 × 1014 Hz). Within this one oc-tave range we can identify more than 7 million colors.Given that the frequency range of the ear is nine timesgreater, one can imagine how many sound colors mightbe possible.

Humans and other animals use sound to commu-nicate, and so it is not surprising that human hearingis most sensitive over the frequency range covered byhuman speech. This is no doubt a logical outcome ofnatural selection. This same match is found throughoutmuch of the animal kingdom. Simple observations show

that small animals generally use high frequencies forcommunication while large animals use low frequen-cies. In Chap. 19, it is shown that song frequency fscales with animal mass M roughly as f ∝ M−1/3.

The least amount of sound energy we can hear is ofthe order of 10−20 J (cf. sensitivity of the eye: about onequantum of light in the middle of the visible spectrum≈ 4 × 10−19 J). The upper limit of the sound pressurethat can be generated is set approximately by atmo-spheric pressure. Such an ultimate sound wave wouldhave a sound pressure level of about 191 dB. In practice,of course, nonlinear effects set in well below this leveland limit the maximum pressure. A large-amplitudesound wave will change waveform and finally break intoa shock, approaching a sawtooth waveform. Nonlineareffects are discussed in Chap. 8.

1.3 Sounds We Cannot Hear: Ultrasound and Infrasound

Sound waves below the frequency of human hearing arecalled infrasound, while sound waves with frequencyabove the range of human hearing are called ultrasound.These sounds have many interesting properties, and arebeing widely studied. Ultrasound is very important inmedical and industrial imaging. It also forms the basisof a growing number of medical procedures, both di-agnostic and therapeutic (see Chap. 21). Ultrasound hasmany applications in scientific research, especially inthe study of solids and fluids (see Chap. 6).

Frequencies as high as 500 MHz have been gener-ated, with a wavelength of about 0.6 µm in air. Thisis on the order of the wavelength of light and withinan order of magnitude of the mean free path of airmolecules. A gas ceases to behave like a continuumwhen the wavelength of sound becomes of the orderof the mean free path, and this sets an upper limit onthe frequency of sound that can propagate. In solidsthe assumption of continuum extends down to the in-termolecular spacing of approximately 0.1 nm, witha limiting frequency of about 1012 Hz. The ultimate limitis actually reached when the wavelength is twice the

spacing of the unit cell of a crystal, where the propaga-tion of multiply scattered sound resembles the diffusionof heat [1.1].

Natural phenomena are prodigious generators ofinfrasound. When Krakatoa exploded, windows wereshattered hundreds of miles away by the infrasonic wave.The ringing of both the Earth and the atmosphere contin-ued for hours. The sudden shock wave of an explosionpropels a complex infrasonic signal far beyond the shat-tered perimeter. Earthquakes generate intense infrasonicwaves. The faster moving P (primary) waves arrive atdistant locations tens of seconds before the destructiveS (secondary) waves. (The P waves carry information;the S waves carry energy.) Certain animals and fish cansense these infrasonic precursors and react with fear andanxiety.

A growing amount of astronomical evidence indi-cates that primordial sound waves at exceedingly lowfrequency propagated in the universe during its first380 000 years while it was a plasma of charged particlesand thus opaque to electromagnetic radiation. Sound istherefore older than light.

1.4 Sounds We Would Rather Not Hear: Environmental Noise Control

Noise has been receiving increasing recognition as oneof our critical environmental pollution problems. Likeair and water pollution, noise pollution increases withpopulation density; in our urban areas, it is a seriousthreat to our quality of life. Noise-induced hearing loss

is a major health problem for millions of people em-ployed in noisy environments. Besides actual hearingloss, humans are affected in many other ways by highlevels of noise. Interference with speech, interruption ofsleep, and other physiological and psychological effects

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of noise have been the subject of considerable study.Noise control is discussed in Chap. 23. The propagationof sound in air in Chap. 4, and building acoustics is thesubject of Chap. 11.

Fortunately for the environment, even the noisiestmachines convert only a small part of their total energyinto sound. A jet aircraft, for example, may producea kilowatt of acoustic power, but this is less than 0.02%of its mechanical output. Automobiles emit approxi-mately 0.001% of their power as sound. Nevertheless,

the shear number of machines operating in our societymakes it crucial that we minimize their sound outputand take measures to prevent the sound from propagat-ing throughout our environment. Although reducing theemitted noise is best done at the source, it is possible,to some extent, to block the transmission of this noisefrom the source to the receiver. Reduction of classroomnoise, which impedes learning in so many schools, is re-ceiving increased attention from government officials aswell as from acousticians [1.2].

1.5 Aesthetic Sound: Music

Music may be defined as an art form using sequencesand clusters of sounds. Music is carried to the listenerby sound waves. The science of musical sound is oftencalled musical acoustics and is discussed in Chap. 15.

Musical acoustics deals with the production ofsound by musical instruments, the transmission ofmusic from the performer to the listener, and theperception and cognition of sound by the listener.Understanding the production of sound by musicalinstruments requires understanding how they vibrateand how they radiate sound. Transmission of soundfrom the performer to the listener involves a study ofconcert hall acoustics (covered in Chaps. 9 and 10)and the recording and reproduction of musical sound

(covered in Chap. 15). Perception of musical soundis based on psychoacoustics, which is discussed inChap. 13.

Electronic musical instruments have become in-creasingly important in contemporary music. Computershave made possible artificial musical intelligence, thesynthesis of new musical sounds and the accurate andflexible re-creation of traditional musical sounds by ar-tificial means. Not only do computers talk and sing andplay music, they listen to us doing the same, and our in-teractions with computers are becoming more like ourinteractions with each other. Electronic and computermusic is discussed in Chap. 17.

1.6 Sound of the Human Voice: Speech and Singing

It is difficult to overstate the importance of the hu-man voice. Of all the members of the animal kingdom,we alone have the power of articulate speech. Speechis our chief means of communication. In addition,the human voice is our oldest musical instrument.Speech and singing, the closely related functions ofthe human voice, are discussed in a unified way inChap. 16.

In the simplest model of speech production, the vo-cal folds act as the source and the vocal tract as a filterof the source sound. According to this model, the spec-trum envelope of speech sound can be thought of as theproduct of two components:

Speech sound = source spectrum × filter function.The nearly triangular waveform of the air flow from

the glottis has a spectrum of harmonics that dimin-ish in amplitude roughly as 1/n2 (i. e., at a rate of

−12 dB/octave). The formants or resonances of the vo-cal tract create the various vowel sounds. The vocal tractcan be shaped by movements of the tongue, the lips, andthe soft palate to tune the formants and articulate thevarious speech sounds.

Sung vowels are fundamentally the same as spokenvowels, although singers do make vowel modificationsin order to improve the musical tone, especially in theirhigh range. In order to produce tones over a wide rangeof pitch, singers use muscular action in the larynx, whichleads to different registers.

Much research has been directed at computer recog-nition and synthesis of speech. Goals of such researchinclude voice-controlled word processors, voice con-trol of computers and other machines, data entry byvoice, etc.In general it is more difficult for a computerto understand language than to speak it.

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1.7 How We Hear: Physiological and Psychological Acoustics

The human auditory system is complex in structure andremarkable in function. Not only does it respond toa wide range of stimuli, but it precisely identifies thepitch, timbre, and direction of a sound. Some of thehearing function is done in the organ we call the ear;some of it is done in the central nervous system as well.

Physiological acoustics, which is discussed inChap. 12, focuses its attention mainly on the peripheralauditory system, especially the cochlea. The dynamicbehavior of the cochlea is a subject of great interest.It is now known that the maximum response along thebasilar membrane of the cochlea has a sharper peak ina living ear than in a dead one.

Resting on the basilar membrane is the delicate andcomplex organ of Corti, which contains several rows ofhair cells to which are attached auditory nerve fibers. Theinner hair cells are mainly responsible for transmittingsignals to the auditory nerve fibers, while the more-numerous outer hair cells act as biological amplifiers.It is estimated that the outer hair cells add about 40 dBof amplification to very weak signals, so that hearingsensitivity decreases by a considerable amount whenthese delicate cells are destroyed by overexposure tonoise.

Our knowledge of the cochlea has now progressedto a point where it is possible to construct and implantelectronic devices in the cochlea that stimulate the au-ditory nerve. A cochlear implant is an electronic devicethat restores partial hearing in many deaf people [1.3]. It

is surgically implanted in the inner ear and activated bya device worn outside the ear. An implant has four basicparts: a microphone, a speech processor and transmit-ter, a receiver inside the ear, and electrodes that transmitimpulses to the auditory nerve and thence to the brain.

Psychoacoustics (psychological acoustics), the sub-ject of Chap. 13, deals with the relationships between thephysical characteristics of sounds and their perceptualattributes, such as loudness, pitch, and timbre.

The threshold of hearing depends upon frequency,the lowest being around 3–4 kHz, where the ear canalhas a resonance, and rising considerably at low fre-quency. Temporal resolution, such as the ability to detectbrief gaps between stimuli or to detect modulation ofa sound, is a subject of considerable interest, as is theability to localize the sound source. Sound localizationdepends upon detecting differences in arrival time anddifferences in intensity at our two ears, as well as spectralcues that help us to localize a source in the median plane.

Most sound that reaches our ears comes from severaldifferent sources. The extent to which we can perceiveeach source separately is sometimes called segregation.One important cue for perceptual separation of nearlysimultaneous sounds is onset and offset disparity. An-other is spectrum change with time. When we listen torapid sequence of sounds, they may be grouped together(fusion) or they may be perceived as different streams(fission). It is difficult to judge the temporal order ofsounds that are perceived in different streams.

1.8 Architectural Acoustics

To many lay people, an acoustician is a person whodesigns concert halls. That is an important part of archi-tectural acoustics, to be sure, but this field incorporatesmuch more. Architectural acousticians seek to under-stand and to optimize the sound environment in roomsand buildings of all types, including those used for work,residential living, education, and leisure. In fact, someof the earliest attempts to optimize sound transmissionwere practised in the design of ancient amphitheaters,and the acoustical design of outdoor spaces for concertsand drama still challenge architects.

In a room, most of the sound waves that reach thelistener’s ear have been reflected by one or more surfacesof the room or by objects in the room. In a typical room,sound waves undergo dozens of reflections before theybecome inaudible. It is not surprising, therefore, that

the acoustical properties of rooms play an importantrole in determining the nature of the sound heard bya listener. Minimizing extraneous noise is an importantpart of the acoustical design of rooms and buildingsof all kinds. Chapter 9 presents the principles of roomacoustics and applies them to performance and assemblyhalls, including theaters and lecture halls, opera halls,concert halls, worship halls, and auditoria.

The subject of concert hall acoustics is almost cer-tain to provoke a lively discussion by both performersand serious listeners. Musicians recognize the impor-tance of the concert hall in communication betweenperformer and listener. Opinions of new halls tend topolarize toward extremes of very good or very bad. Inconsidering concert and opera halls, it is important toseek a common language for musicians and acousticians

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Introduction to Acoustics 1.10 Medical Acoustics 5

in order to understand how objective measurements re-late to subjective qualities [1.4,5]. Chapter 10 discussessubjective preference theory and how it relates to concerthall design.

Two acoustical concerns in buildings are providingthe occupants with privacy and with a quiet environ-ment, which means dealing with noise sources withinthe building as well as noise transmitted from outside.The most common noise sources in buildings, other thanthe inhabitants, are related to heating, ventilating, and

air conditioning (HVAC) systems, plumbing systems,and electrical systems. Quieting can best be done atthe source, but transmission of noise throughout thebuilding must also be prevented. The most commonexternal noise sources that affect buildings are thoseassociated with transportation, such as motor vehicles,trains, and airplanes. There is no substitute for mas-sive walls, although doors and windows must receiveattention as well. Building acoustics is discussed inChap. 11.

1.9 Harnessing Sound: Physical and Engineering Acoustics

It is sometimes said that physicists study nature, en-gineers attempt to improve it. Physical acoustics andengineering acoustics are two very important areas ofacoustics. Physical acousticians investigate a wide rangeof scientific phenomena, including the propagation ofsound in solids, liquids, and gases, and the way soundinteracts with the media through which it propagates.The study of ultrasound and infrasound are especiallyinteresting. Physical acoustics is discussed in Chap. 6.

Acoustic techniques have been widely used to studythe structural and thermodynamic properties of materialsat very low temperatures. Studying the propagation of ul-trasound in metals, dielectric crystals, amorphous solids,and magnetic materials has yielded valuable informationabout their elastic, structural and other properties. Es-pecially interesting has been the propagation of soundin superfluid helium. Second sound, an unusual type oftemperature wave, was discovered in 1944, and sincethat time so-called third sound, fourth sound, and fifthsound have been described [1.6].

Nonlinear effects in sound are an important partof physical acoustics. Nonlinear effects of interestinclude waveform distortion, shock-wave formation, in-teractions of sound with sound, acoustic streaming,cavitation, and acoustic levitation. Nonlinearity leadsto distortion of the sinusoidal waveform of a soundwave so that it becomes nearly triangular as the shockwave forms. On the other hand, local disturbances, calledsolitons, retain their shape over large distances.

The study of the interaction of sound and light, calledacoustooptics, is an interesting field in physical acoustics

that has led to several practical devices. In an acoustoop-tic modulator, for example, sound waves form a sortof moving optical diffraction grating that diffracts andmodulates a laser beam.

Sonoluminescence is the name given to a processby which intense sound waves can generate light. Thelight is emitted by bubbles in a liquid excited by sound.The observed spectra of emitted light seem to indicatetemperatures hotter than the surface of the sun. Someexperimental evidence indicates that nuclear fusion maytake place in bubbles in deuterated acetone irradiatedwith intense ultrasound.

Topics of interest in engineering acoustics covera wide range and include: transducers and arrays, un-derwater acoustic systems, acoustical instrumentation,audio engineering, acoustical holography and acousti-cal imaging, ultrasound, and infrasound. Several of thesetopics are covered in Chaps. 5, 18, 24, 25, 26, 27, and 28.Much effort has been directed into engineering increas-ingly small transducers to produce and detect sound.Microphones are being fabricated on silicon chips asparts of integrated circuits.

The interaction of sound and heat, called thermoa-coustics, is an interesting field that applies principlesof physical acoustics to engineering systems. The ther-moacoustic effect is the conversion of sound energy toheat or visa versa. In thermoacoustic processes, acousticpower can pump heat from a region of low temperatureto a region of higher temperature. This can be used toconstruct heat engines or refrigerators with no movingparts. Thermoacoustics is discussed in Chap. 7.

1.10 Medical Acoustics

Two uses of sound that physicians have employed formany years are auscultation, listening to the body with

a stethoscope, and percussion, sound generation by thestriking the chest or abdomen to assess transmission or

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resonance. The most exciting new developments in med-ical acoustics, however, involve the use of ultrasound,both diagnostic imaging and therapeutic applications.

There has been a steady improvement in the qual-ity of diagnostic ultrasound imaging. Two importantcommercial developments have been the advent ofreal-time three-dimensional (3-D) imaging and the de-velopment of hand-held scanners. Surgeons can nowcarry out procedures without requiring optical access.Although measurements on isolated tissue samples showthat acoustic attenuation and backscatter correlate withpathology, implementing algorithms to obtain this infor-mation on a clinical scanner is challenging at the presenttime.

The therapeutic use of ultrasound has blossomed inrecent years. Shock-wave lithotripsy is the predominantsurgical operation for the treatment of kidney stones.Shock waves also appear to be effective at helping healbroken bones. High-intensity focused ultrasound is usedto heat tissue selectivity so that cells can be destroyed ina local region. Ultrasonic devices appear to hold promisefor treating glaucoma, fighting cancer, and controllinginternal bleeding. Advanced therapies, such as punctur-ing holes in the heart, promoting localized drug delivery,and even carrying out brain surgery through an intactskull appear to be feasible with ultrasound [1.7].

Other applications of medical ultrasound are in-cluded in Chap. 21.

1.11 Sounds of the Sea

Oceans cover more than 70% of the Earth’s surface.Sound waves are widely used to explore the oceans, be-cause they travel much better in sea water than lightwaves. Likewise, sound waves are used, by humans anddolphins alike, to communicate under water, becausethey travel much better than radio waves. Acousticaloceanography has many military, as well as commercialapplications. Much of our understanding of underwatersound propagation is a result of research conducted dur-ing and following World War II. Underwater acousticsis discussed in Chap. 5.

The speed of sound in water, which is about1500 m/s, increases with increasing static pressure byabout 1 part per million per kilopascal, or about 1% per1000 m of depth, assuming temperature remains con-stant. The variation with temperature is an increase ofabout 2% per ◦C temperature rise. Refraction of sound,due to these changes in speed, along with reflection atthe surface and the bottom, lead to waveguides at vari-ous ocean depths. During World War II, a deep channel

was discovered in which sound waves could travel dis-tances in excess of 3000 km. This phenomenon gaverise to the deep channel or sound fixing and ranging(SOFAR) channel, which could be used to locate, byacoustic means, airmen downed at sea.

One of the most important applications of underwa-ter acoustics is sound navigation and ranging (SONAR).The purpose of most sonar systems is to detect and local-ize a target, such as submarines, mines, fish, or surfaceships. Other SONARs are designed to measure somequantity, such as the ocean depth or the speed of oceancurrents.

An interesting phenomenon called cavitation oc-curs when sound waves of high intensity propagatethrough water. When the rarefaction tension phase ofthe sound wave is great enough, the medium rup-tures and cavitation bubbles appear. Cavitation bubblescan be produced by the tips of high-speed propellers.Bubbles affect the speed of sound as well as its attenu-ation [1.7, 8].

References

1.1 U. Ingard: Acoustics. In: Handbook of Physics, 2ndedn., ed. by E.U. Condon, H. Odishaw (McGraw-Hill,New York 1967)

1.2 B. Seep, R. Glosemeyer, E. Hulce, M. Linn, P. Aytar,R. Coffeen: Classroom Acoustics (Acoustical Society ofAmerica, Melville 2000, 2003)

1.3 M.F. Dorman, B.S. Wilson: The design and func-tion of cochlear implants, Am. Scientist 19, 436–445(2004)

1.4 L.L. Beranek: Music, Acoustics and Architecture (Wi-ley, New York 1962)

1.5 L. Beranek: Concert Halls and Opera Houses, 2ndedn. (Springer, Berlin, Heidelberg, New York 2004)

1.6 G. Williams: Low-temperature acoustics. In:McGraw-Hill Encyclopedia of Physics, 2nd edn., ed.by S. Parker (McGraw-Hill, New York 1993)

1.7 R.O. Cleveland: Biomedical ultrasound/bioresponseto vibration. In: ASA at 75, ed. by H.E. Bass, W.J. Ca-vanaugh (Acoustical Society of America, Melville2004)

1.8 H. Medwin, C.S. Clay: Fundamentals of AcousticalOceanography (Academic, Boston 1998)

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PropagatPart APart A Propagation of Sound

2 A Brief History of AcousticsThomas D. Rossing, Stanford, USA

3 Basic Linear AcousticsAlan D. Pierce, Boston, USA

4 Sound Propagation in the AtmosphereKeith Attenborough, Hull, UK

5 Underwater AcousticsWilliam A. Kuperman, La Jolla, USAPhilippe Roux, Grenoble, France

9

A Brief History2. A Brief History of Acoustics

Although there are certainly some good historicaltreatments of acoustics in the literature, it stillseems appropriate to begin a handbook ofacoustics with a brief history of the subject. Webegin by mentioning some important experimentsthat took place before the 19th century. Acoustics inthe 19th century is characterized by describing thework of seven outstanding acousticians: Tyndall,von Helmholtz, Rayleigh, Stokes, Bell, Edison, andKoenig. Of course this sampling omits the mentionof many other outstanding investigators.

To represent acoustics during the 20th century,we have selected eight areas of acoustics,again not trying to be all-inclusive. We selectthe eight areas represented by the first eighttechnical areas in the Acoustical Society ofAmerica. These are architectural acoustics, physicalacoustics, engineering acoustics, structuralacoustics, underwater acoustics, physiologicaland psychological acoustics, speech, and musicalacoustics. We apologize to readers whose maininterest is in another area of acoustics. It is, afterall, a broad interdisciplinary field.

2.1 Acoustics in Ancient Times .................... 9

2.2 Early Experiments on Vibrating Strings,Membranes and Plates ......................... 10

2.3 Speed of Sound in Air .......................... 10

2.4 Speed of Soundin Liquids and Solids............................ 11

2.5 Determining Frequency ........................ 11

2.6 Acoustics in the 19th Century ................ 122.6.1 Tyndall .................................... 122.6.2 Helmholtz ................................ 122.6.3 Rayleigh................................... 132.6.4 George Stokes ........................... 132.6.5 Alexander Graham Bell .............. 142.6.6 Thomas Edison.......................... 142.6.7 Rudolph Koenig ........................ 14

2.7 The 20th Century ................................. 152.7.1 Architectural Acoustics ............... 152.7.2 Physical Acoustics ...................... 162.7.3 Engineering Acoustics ................ 182.7.4 Structural Acoustics ................... 192.7.5 Underwater Acoustics ................ 192.7.6 Physiological

and Psychological Acoustics ........ 202.7.7 Speech ..................................... 212.7.8 Musical Acoustics ...................... 21

2.8 Conclusion .......................................... 23

References .................................................. 23

2.1 Acoustics in Ancient Times

Acoustics is the science of sound. Although sound wavesare nearly as old as the universe, the scientific study ofsound is generally considered to have its origin in ancientGreece. The word acoustics is derived from the Greekword akouein, to hear, although Sauveur appears to havebeen the first person to apply the term acoustics to thescience of sound in 1701 [2.1].

Pythagoras, who established mathematics in Greekculture during the sixth century BC, studied vibratingstrings and musical sounds. He apparently discoveredthat dividing the length of a vibrating string into simpleratios produced consonant musical intervals. According

to legend, he also observed how the pitch of the stringchanged with tension and the tones generated by strikingmusical glasses, but these are probably just legends [2.2].

Although the Greeks were certainly aware of the im-portance of good acoustical design in their many finetheaters, the Roman architect Vitruvius was the firstto write about it in his monumental De Architectura,which includes a remarkable understanding and analy-sis of theater acoustics: “We must choose a site in whichthe voice may fall smoothly, and not be returned by re-flection so as to convey an indistinct meaning to theear.”

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10 Part A Propagation of Sound

2.2 Early Experiments on Vibrating Strings, Membranes and Plates

Much of early acoustical investigations were closelytied to musical acoustics. Galileo reviewed the relation-ship of the pitch of a string to its vibrating length, andhe related the number of vibrations per unit time topitch. Joseph Sauveur made more-thorough studies offrequency in relation to pitch. The English mathemati-cian Brook Taylor provided a dynamical solution for thefrequency of a vibrating string based on the assumedcurve for the shape of the string when vibrating in itsfundamental mode. Daniel Bernoulli set up a partialdifferential equation for the vibrating string and ob-tained solutions which d’Alembert interpreted as wavestraveling in both directions along the string [2.3].

The first solution of the problem of vibrating mem-branes was apparently the work of S. D. Poisson, andthe circular membrane was handled by R. F. A. Clebsch.Vibrating plates are somewhat more complex than vi-brating membranes. In 1787 E. F. F. Chladni describedhis method of using sand sprinkled on vibrating plates toshow nodal lines [2.4]. He observed that the addition ofone nodal circle raised the frequency of a circular plate

Fig. 2.1 Chladni patterns on a circular plate. The first four have two, three, four, and five nodal lines but no nodal circles;the second four have one or two nodal circles

by about the same amount as adding two nodal diam-eters, a relationship that Lord Rayleigh called Chladni’slaw. Sophie Germain wrote a fourth-order equation todescribe plate vibrations, and thus won a prize providedby the French emperor Napoleon, although Kirchhofflater gave a more accurate treatment of the boundaryconditions. Rayleigh, of course, treated both membranesand plates in his celebrated book Theory of Sound [2.5].

Chladni generated his vibration patterns by “strew-ing sand” on the plate, which then collected along thenodal lines. Later he noticed that fine shavings fromthe hair of his violin bow did not follow the sandto the nodes, but instead collected at the antinodes.Savart noted the same behavior for fine lycopodiumpowder [2.6]. Michael Faraday explained this as beingdue to acoustic streaming [2.7]. Mary Waller publishedseveral papers and a book on Chladni patterns, in whichshe noted that particle diameter should exceed 100 µmin order to collect at the nodes [2.8]. Chladni figures ofsome of the many vibrational modes of a circular plateare shown in Fig. 2.1.

2.3 Speed of Sound in Air

From earliest times, there was agreement that sound ispropagated from one place to another by some activity ofthe air. Aristotle understood that there is actual motionof air, and apparently deduced that air is compressed.The Jesuit priest Athanasius Kircher was one of the firstto observe the sound in a vacuum chamber, and sincehe could hear the bell he concluded that air was notnecessary for the propagation of sound. Robert Boyle,however, repeated the experiment with a much improvedpump and noted the much-observed decrease in soundintensity as the air is pumped out. We now know thatsound propagates quite well in rarified air, and that thedecrease in intensity at low pressure is mainly due to

the impedance mismatch between the source and themedium as well as the impedance mismatch at the wallsof the container.

As early as 1635, Gassendi measured the speed ofsound using firearms and assuming that the light of theflash is transmitted instantaneously. His value came outto be 478 m/s. Gassendi noted that the speed of sounddid not depend on the pitch of the sound, contrary tothe view of Aristotle, who had taught that high notesare transmitted faster than low notes. In a more carefulexperiment, Mersenne determined the speed of sound tobe 450 m/s [2.9]. In 1650, G. A. Borelli and V. Viviani ofthe Accademia del Cimento of Florence obtained a value

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A Brief History of Acoustics 2.5 Determining Frequency 11

of 350 m/s for the speed of sound [2.10]. Another Italian,G. L. Bianconi, showed that the speed of sound in airincreases with temperature [2.11].

The first attempt to calculate the speed of soundthrough air was apparently made by Sir Isaac Newton.He assumed that, when a pulse is propagated througha fluid, the particles of the fluid move in simple har-monic motion, and that if this is true for one particle,it must be true for all adjacent ones. The result is thatthe speed of sound is equal to the square root of the ra-tio of the atmospheric pressure to the density of the air.This leads to values that are considerably less than thosemeasured by Newton (at Trinity College in Cambridge)and others.

In 1816, Pierre Simon Laplace suggested that inNewton’s and Lagrange’s calculations an error had beenmade in using for the volume elasticity of the air the pres-sure itself, which is equivalent to assuming the elasticmotions of the air particles take place at constant temper-ature. In view of the rapidity of the motions, it seemedmore reasonable to assume that the compressions andrarefactions follow the adiabatic law. The adiabatic elas-ticity is greater than the isothermal elasticity by a factorγ , which is the ratio of the specific heat at constantpressure to that at constant volume. The speed of soundshould thus be given by c= (γ p/ρ)1/2, where p is thepressure and ρ is the density. This gives much betteragreement with experimental values [2.3].

2.4 Speed of Sound in Liquids and Solids

The first serious attempt to measure the speed of soundin liquid was probably that of the Swiss physicistDaniel Colladon, who in 1826 conducted studies in LakeGeneva. In 1825, the Academy of Sciences in Paris hadannounced as the prize competition for 1826 the meas-urement of the compressibility of the principal liquids.Colladon measured the static compressibility of severalliquids, and he decided to check the accuracy of hismeasurements by measuring the speed of sound, whichdepends on the compressibility. The compressibility ofwater computed from the speed of sound turned out tobe very close to the statically measured values [2.12].Oh yes, he won the prize from the Academy.

In 1808, the French physicist J. B. Biot measured thespeed of sound in a 1000 m long iron water pipe in Parisby direct timing of the sound travel [2.13]. He com-pared the arrival times of the sound through the metaland through the air and determined that the speed ismuch greater in the metal. Chladni had earlier studiedthe speed of sound in solids by noting the pitch em-anating from a struck solid bar, just as we do today.He deduced that the speed of sound in tin is about 7.5times greater than in air, while in copper it was about12 times greater. Biot’s values for the speed in metalsagreed well with Chladni’s.

2.5 Determining Frequency

Much of the early research on sound was tied to mu-sical sound. Vibrating strings, membranes, plates, andair columns were the bases of various musical instru-ments. Music emphasized the importance of ratios forthe different tones. A string could be divided into halvesor thirds or fourths to give harmonious pitches. It wasalso known that pitch is related to frequency. MarinMersenne (1588–1648) was apparently the first to de-termine the frequency corresponding to a given pitch.By working with a long rope, he was able determine thefrequency of a standing wave on the length, mass, andtension of the rope. He then used a short wire under ten-sion and from his rope formula he was able to computethe frequency of oscillation [2.14]. The relationship be-

tween pitch and frequency was later improved by JosephSauveur, who counted beats between two low-pitchedorgan pipes differing in pitch by a semitone. Sauveurdeduced that “the relation between sounds of low andhigh pitch is exemplified in the ratio of the numbers of vi-brations which they both make in the same time.” [2.1].He recognized that two sounds differing a musical fifthhave frequencies in the ratio of 3:2. We have alreadycommented that Sauveur was the first to apply the termacoustics to the science of sound. “I have come then tothe opinion that there is a science superior to music, andI call it acoustics; it has for its object sound in general,whereas music has for its objects sounds agreeable tothe ear.” [2.1]

PartA

2.5