Sound Propagation: An Impedance Based Approach

358 Pages·2010·4.08 MB·English

by  Kim Y.-H.

SOUND PROPAGATION
AN IMPEDANCE BASED APPROACH
Sound Propagation: An Impedance Based Approa c h Yang-Hann Kim
© 2010 John Wiley & Sons (Asia) Pte Ltd. ISBN: 978-0-470-82583-9

SOUND PROPAGATION
AN IMPEDANCE BASED APPROACH
Yang-Hann Kim
Korea Advanced Instituteof Science and Technology (KAIST),Republic ofKorea
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Kim,Yang-Hann.
Soundpropagation:animpedancebasedapproach/Yang-HannKim.
p.cm.
Includesbibliographicalreferencesandindex.
ISBN978-0-470-82583-9(cloth)
1. Acousticimpedance.2. Sound–Transmission.3. Sound-waves. I.Title.
QC233.K482010
534–dc22
2010010282
ISBN978-0-470-82583-9(HB)
Typesetin10/12ptTimesbyThomsonDigital,Noida,India.
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Formy children, Jue-Hee, Juelie andJueseok,
The very beginningof all hopes andthe source of love
Andespecially for my beloved wife, Eun-wha,
In commemoration ofour 30th wedding anniversary

Contents
Preface xi
Acknowledgments xv
1 Vibration and Waves 1
1.1 Introduction/Study Objectives 1
1.2 From String Vibration toWave 1
1.3 One-dimensional WaveEquation 7
1.4 SpecificImpedance (Reflectionand Transmission) 10
1.5 The GoverningEquation of aString 14
1.6 ForcedResponse ofa String: Driving Point Impedance 17
1.7 Wave EnergyPropagation along a String 22
1.8 Chapter Summary 25
1.9 Essentials ofVibration and Waves 25
1.9.1 Single- and Two-degree ofFreedomVibration Systems 25
1.9.2 FourierSeriesand Fourier Integral 34
1.9.3 WavePhenomena ofBar, Beam, Membrane, and Plate 36
Exercises 59
2 Acoustic Wave EquationandIts Basic PhysicalMeasures 69
2.1 Introduction/Study Objectives 69
2.2 One-dimensional Acoustic WaveEquation 69
2.3 Acoustic Intensity andEnergy 77
2.4 The Units ofSound 85
2.5 Analysis Methods ofLinearAcoustic Wave Equation 96
2.6 Solutionsof the Wave Equation 103
2.7 Chapter Summary 110
2.8 Essentials ofWave Equations andBasic Physical Measures 110
2.8.1 Three-dimensional Acoustic WaveEquation 110
2.8.2 Velocity Potential Function 116
2.8.3 ComplexIntensity 116
2.8.4 Singular Sources 118
Exercises 125
viii Contents
3 Waves on a Flat Surfaceof Discontinuity 129
3.1 Introduction/Study Objectives 129
3.2 Normal Incidenceon a FlatSurface of Discontinuity 129
3.3 The Mass Law(Reflection and Transmission dueto aLimpWall) 134
3.4 Transmission Loss at aPartition 140
3.5 Oblique Incidence(Snell’s Law) 144
3.6 Transmission and Reflection ofan InfinitePlate 149
3.7 The Reflection andTransmissionof aFinite Structure 153
3.8 Chapter Summary 156
3.9 Essentials ofSound Waves on aFlat Surface ofDiscontinuity 156
3.9.1 Locally ReactingSurface 156
3.9.2 Transmission Loss by a Partition 159
3.9.3 Transmission andReflection in Layers 159
3.9.4 Snell’s LawWhen the IncidenceAngleis Larger
than the Critical Angle 168
3.9.5 Transmission Coefficientofa Finite Plate 169
Exercises 172
4 Radiation, Scattering,and Diffraction 177
4.1 Introduction/Study Objectives 177
4.2 Radiation of aBreathing Sphere and a TremblingSphere 178
4.3 Radiation from aBaffled Piston 188
4.4 Radiation from aFinite Vibrating Plate 196
4.5 Diffraction andScattering 201
4.6 Chapter Summary 213
4.7 Essentials ofRadiation,Scattering, and Diffraction 214
4.7.1 Definitionsof PhysicalQuantities RepresentingDirectivity 214
4.7.2 TheRadiatedSoundFieldfromanInfinitelyBaffledCircularPiston 217
4.7.3 SoundFieldat an ArbitraryPosition Radiated byan Infinitely
BaffledCircular Piston 218
4.7.4 Understanding Radiation, Scattering, andDiffraction Using the
Kirchhoff–Helmholtz IntegralEquation 219
4.7.5 Scattered Sound FieldUsing the Rayleigh Integral Equation 236
4.7.6 Theoretical Approach toDiffraction Phenomenon 237
Exercises 265
5 Acoustics in a Closed Space 273
5.1 Introduction/Study Objectives 273
5.2 Acoustic Characteristics of aClosed Space 273
5.3 Theory for AcousticallyLargeSpace (Sabine’s theory) 274
5.4 Direct and ReverberantField 282
5.5 Analysis Methods for aClosed Space 287
5.6 Characteristics of Sound ina Small Space 292
5.7 Duct Acoustics 302
5.8 Chapter Summary 312
Contents ix
5.9 Essentials ofAcoustics ina Closed Space 313
5.9.1 Methodsfor Measuring Absorption Coefficient 313
5.9.2 Various Reverberation TimePrediction Formulae 317
5.9.3 Sound Pressure DistributioninClosed 3D Space Using
Mode Function 319
5.9.4 Analytic Solution of1D CavityInterior Fieldwith Any
Boundary Condition 320
5.9.5 Helmholtz Resonator Array Panels 323
Exercises 335
Index 339