Elsevier S & T

Fourier Acoustics: Sound Radiation and Nearfield Acoustical Holography

Williams, Earl G.

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Table of contents
  • Cover
  • Contentsv
  • Prefacexi
  • Chapter 1. Fourier Transforms & Special Functions1
  • 1.1 Introduction1
  • 1.2 The Fourier Transform1
  • 1.3 Fourier Series4
  • 1.4 Fourier–Bessel (Hankel) Transforms5
  • 1.5 The Dirac Delta Function6
  • 1.6 The Rectangle Function7
  • 1.7 The Comb Function8
  • 1.8 Continuous Fourier Transform and the DFT8
  • Problems13
  • Chapter 2. Plane Waves15
  • 2.1 Introduction15
  • 2.2 The Wave Equation and Euler's Equation15
  • 2.3 Instantaneous Acoustic Intensity17
  • 2.4 Steady State18
  • 2.5 Time Averaged Acoustic Intensity19
  • 2.6 Plane Wave Expansion20
  • 2.7 Infinite Plate Vibrating in a Normal Mode26
  • 2.8 Wavenumber Space: k-space27
  • 2.9 The Angular Spectrum: Fourier Acoustics31
  • 2.10 Derivation of Rayleigh's Integrals34
  • 2.11 Farfield Radiation: Planar Sources38
  • 2.12 Radiated Power52
  • 2.13 Vibration & Radiation: Infinite Point-driven Plate56
  • 2.14 Vibration & Radiation: Finite, Simply Supported Plate62
  • 2.15 Supersonic Intensity77
  • Problems83
  • Chapter 3. The Inverse Problem: Planar NAH89
  • 3.1 Introduction89
  • 3.2 Overview of the Theory90
  • 3.3 Presentation of Theory for a One-Dimensional Radiator91
  • 3.4 Ill Conditioning Due to Measurement Noise93
  • 3.5 The k-space Filter94
  • 3.6 Modification of the Filter Shape97
  • 3.7 Measurement Noise and the Standoff Distance98
  • 3.8 Determination of the k-space Filter100
  • 3.9 Finite Measurement Aperture Effects103
  • 3.10 Discretization and Aliasing105
  • 3.11 Use of the DFT to Solve the Holography Equation107
  • 3.12 Reconstruction of Other Quantities112
  • Problems113
  • Chapter 4. Cylindrical Waves115
  • 4.1 Introduction115
  • 4.2 The Wave Equation115
  • 4.3 General Solution121
  • 4.4 The Helical Wave Spectrum: Fourier Acoustics125
  • 4.5 The Rayleigh-like Integrals133
  • 4.6 Farfield Radiation - Cylindrical Sources137
  • 4.7 Radiated Power147
  • Problems148
  • Chapter 5. The Inverse Problem: Cylindrical NAH149
  • 5.1 Introduction149
  • 5.2 Overview of the Inverse Problem149
  • 5.3 Computer Implementation of NAH154
  • 5.4 Experimental Results160
  • Problems181
  • Chapter 6. Spherical Waves183
  • 6.1 Introduction183
  • 6.2 The Wave Equation183
  • 6.3 The Angle Functions186
  • 6.4 Radial Functions193
  • 6.5 Multipoles197
  • 6.6 Spherical Harmonic Directivity Patterns204
  • 6.7 General Solution for Exterior Problems206
  • 6.8 General Solution for Interior Problems217
  • 6.9 Transient Radiation - Exterior Problems221
  • 6.10 Scattering from Spheres224
  • Problems232
  • Chapter 7. Spherical NAH235
  • 7.1 Introduction235
  • 7.2 Formulation of the Inverse Problem- Exterior Domain236
  • 7.3 Interior NAH238
  • 7.4 Scattering Nearfield Holography245
  • Problems249
  • Chapter 8. Green Functions & the Helmholtz Integral251
  • 8.1 Introduction251
  • 8.2 Green's Theorem251
  • 8.3 The Interior Helmholtz Integral Equation252
  • 8.4 HIE for Radiation Problems (Exterior Domain)260
  • 8.5 HIE for Scattering Problems262
  • 8.6 Green Functions & the Inhomogeneous Wave Equation264
  • 8.7 Simple Source Formulation267
  • 8.8 The Dirichlet and Neumann Green Functions272
  • 8.9 Construction by Eigenfunction Expansion277
  • 8.10 Evanescent Neumann & Dirichlet Green Functions281
  • 8.11 Arbitrarily Shaped Bodies288
  • 8.12 Conformal NAH for Arbitrary Geometry291
  • Problems293
  • Index296
Book details
  • Vendor Elsevier S & T
  • SKU 9780127539607
  • ISBN-13 9780080506906
  • Author Williams, Earl G.
  • Category Science
  • Subject Acoustics & Sound

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Description eBook delivery & access Reviews
Intended a both a textbook and a reference, Fourier Acoustics develops the theory of sound radiation uniquely from the viewpoint of Fourier Analysis. This powerful perspective of sound radiation provides the reader with a comprehensive and practical understanding which will enable him or her to diagnose and solve sound and vibration problems in the 21st Century. As a result of this perspective, Fourier Acoustics is able to present thoroughly and simply, for the first time in book form, the theory of nearfield acoustical holography, an important technique which has revolutionised the measurement of sound. Relying little on material outside the book, Fourier Acoustics will be invaluable as a graduate level text as well as a reference for researchers in academia and industry.

Key Features
* The physics of wave propogation and sound vibration in homogeneous media
*Acoustics, such as radiation of sound, and radiation from vibrating surfaces
*Inverse problems, such as the theory of nearfield acoustical holography
*Mathematics of specialized functions, such as spherical harmonics