Preface ........................................................ XI
Acknowledgments ................................................ XV
1 Vibration and Waves .......................................... 1
1.1 Introduction/Study Objectives ........................... 1
1.2 From String Vibration to Wave ........................... 1
1.3 One-dimensional Wave Equation ........................... 7
1.4 Specific Impedance (Reflection and Transmission) ....... 10
1.5 The Governing Equation of a String ..................... 14
1.6 Forced Response of a String: Driving Point Impedance ... 17
1.7 Wave Energy Propagation along a String ................. 22
1.8 Chapter Summary ........................................ 25
1.9 Essentials of Vibration and Waves ...................... 25
1.9.1 Single-and Two-degree of Freedom Vibration
Systems ......................................... 25
1.9.2 Fourier Series and Fourier Integral ............. 34
1.9.3 Wave Phenomena of Bar, Beam, Membrane, and
Plate ........................................... 36
Exercises ................................................... 59
2 Acoustic Wave Equation and Its Basic Physical Measures ...... 69
2.1 Introduction/Study Objectives .......................... 69
2.2 One-dimensional Acoustic Wave Equation ................. 69
2.3 Acoustic Intensity and Energy .......................... 77
2.4 The Units of Sound ..................................... 85
2.5 Analysis Methods of Linear Acoustic Wave Equation ...... 96
2.6 Solutions of the Wave Equation ........................ 103
2.7 Chapter Summary ....................................... 110
2.8 Essentials of Wave Equations and Basic Physical
Measures .............................................. 110
2.8.1 Three-dimensional Acoustic Wave Equation ....... 110
2.8.2 Velocity Potential Function .................... 116
2.8.3 Complex Intensity .............................. 116
2.8.4 Singular Sources ............................... 118
Exercises .................................................. 125
3 Waves on a Flat Surface of Discontinuity ................... 129
3.1 Introduction/Study Objectives ......................... 129
3.2 Normal Incidence on a Flat Surface of Discontinuity ... 129
3.3 The Mass Law (Reflection and Transmission due to a
Limp Wall) ............................................ 134
3.4 Transmission Loss at a Partition ...................... 140
3.5 Oblique Incidence (Snell's Law) ....................... 144
3.6 Transmission and Reflection of an Infinite Plate ...... 149
3.7 The Reflection and Transmission of a Finite
Structure ............................................. 153
3.8 Chapter Summary ....................................... 156
3.9 Essentials of Sound Waves on a Flat Surface of
Discontinuity ......................................... 156
3.9.1 Locally Reacting Surface ....................... 156
3.9.2 Transmission Loss by a Partition ............... 159
3.9.3 Transmission and Reflection in Layers .......... 159
3.9.4 Snell's Law When the Incidence Angle is
Larger than the Critical Angle ................. 168
3.9.5 Transmission Coefficient of a Finite Plate ..... 169
Exercises .................................................. 172
4 Radiation, Scattering, and Diffraction ..................... 177
4.1 Introduction/Study Objectives ......................... 177
4.2 Radiation of a Breathing Sphere and a Trembling
Sphere ................................................ 178
4.3 Radiation from a Baffled Piston ....................... 188
4.4 Radiation from a Finite Vibrating Plate ............... 196
4.5 Diffraction and Scattering ............................ 201
4.6 Chapter Summary ....................................... 213
4.7 Essentials of Radiation, Scattering, and
Diffraction ........................................... 214
4.7.1 Definitions of Physical Quantities
Representing Directivity ....................... 214
4.7.2 The Radiated Sound Field from an Infinitely
Baffled Circular Piston ....................... 217
4.7.3 Sound Field at an Arbitrary Position Radiated
by an Infinitely Baffled Circular Piston ...... 218
4.7.4 Understanding Radiation, Scattering, and
Diffraction Using the Kirchhoff-Helmholtz
Integral Equation .............................. 219
4.7.5 Scattered Sound Field Using the Rayleigh
Integral Equation .............................. 236
4.7.6 Theoretical Approach to Diffraction
Phenomenon ..................................... 237
Exercises .................................................. 265
5 Acoustics in a Closed Space ................................ 273
5.1 Introduction/Study Objectives ......................... 273
5.2 Acoustic Characteristics of a Closed Space ............ 273
5.3 Theory for Acoustically Large Space (Sabine's
theory) ............................................... 274
5.4 Direct and Reverberant Field .......................... 282
5.5 Analysis Methods for a Closed Space ................... 287
5.6 Characteristics of Sound in a Small Space ............. 292
5.7 Duct Acoustics ........................................ 302
5.8 Chapter Summary ....................................... 312
5.9 Essentials of Acoustics in a Closed Space ............. 313
5.9.1 Methods for Measuring Absorption Coefficient ... 313
5.9.2 Various Reverberation Time Prediction
Formulae ....................................... 317
5.9.3 Sound Pressure Distribution in Closed 3D
Space Using Mode Function ...................... 319
5.9.4 Analytic Solution of ID Cavity Interior Field
with Any Boundary Condition .................... 320
5.9.5 Helmholtz Resonator Array Panels ............... 323
Exercises .................................................. 335
Index ......................................................... 339
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