Fourier Acoustics

Fourier Acoustics

by Earl G. Williams
Released June 1999
Publisher(s): Academic Press
ISBN: 9780080506906

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Book description

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

Table of contents

  1. Cover image
  2. Title page
  3. Table of Contents
  4. Dedication
  5. Copyright
  6. Preface
  7. Chapter 1: Fourier Transforms & Special Functions
    1. 1.1 Introduction
    2. 1.2 The Fourier Transform
    3. 1.3 Fourier Series
    4. 1.4 Fourier-Bessel (Hankel) Transforms
    5. 1.5 The Dirac Delta Function
    6. 1.6 The Rectangle Function
    7. 1.7 The Comb Function
    8. 1.8 Continuous Fourier Transform and the DFT
    9. Problems
  8. Chapter 2: Plane Waves
    1. 2.1 Introduction
    2. 2.2 The Wave Equation and Euler’s Equation
    3. 2.3 Instantaneous Acoustic Intensity
    4. 2.4 Steady State
    5. 2.5 Time Averaged Acoustic Intensity
    6. 2.6 Plane Wave Expansion
    7. 2.7 Infinite Plate Vibrating in a Normal Mode
    8. 2.8 Wavenumber Space: k-space
    9. 2.9 The Angular Spectrum: Fourier Acoustics
    10. 2.10 Derivation of Rayleigh’s Integrals
    11. 2.11 Farfield Radiation: Planar Sources
    12. 2.12 Radiated Power
    13. 2.13 Vibration and Radiation from an Infinite Point-driven Plate
    14. 2.14 Vibration and Radiation of a Finite, Simply Supported Plate
    15. 2.15 Supersonic Intensity
    16. Problems
  9. Chapter 3: The Inverse Problem: Planar Nearfield Acoustical Holography
    1. 3.1 Introduction
    2. 3.2 Overview of the Theory
    3. 3.3 Presentation of Theory for a One-Dimensional Radiator
    4. 3.4 Ill Conditioning Due to Measurement Noise
    5. 3.5 The k-space Filter
    6. 3.5.1 Examples
    7. 3.6 Modification of the Filter Shape
    8. 3.7 Measurement Noise and the Standoff Distance
    9. 3.8 Determination of the Cutoff Frequency for the k-space Filter
    10. 3.9 Finite Measurement Aperture Effects
    11. 3.10 Discretization and Aliasing
    12. 3.11 Use of the DFT to Solve the Holography Equation
    13. 3.12 Reconstruction of Other Quantities
    14. 3.12.1 Time Domain
    15. Problems
  10. Chapter 4: Cylindrical Waves
    1. 4.1 Introduction
    2. 4.2 The Wave Equation
    3. 4.3 General Solution
    4. 4.4 The Helical Wave Spectrum: Fourier Acoustics
    5. 4.5 The Rayleigh-like Integrals
    6. 4.6 Farfield Radiation - Cylindrical Sources
    7. 4.7 Radiated Power
    8. Problems
  11. Chapter 5: The Inverse Problem: Cylindrical NAH
    1. 5.1 Introduction
    2. 5.2 Overview of the Inverse Problem
    3. 5.3 Implementation of Cylindrical Nearfield Acoustical Holography
    4. 5.4 Experimental Results
    5. Problems
  12. Chapter 6: Spherical Waves
    1. 6.1 Introduction
    2. 6.2 The Wave Equation
    3. 6.3 The Angle Functions
    4. 6.4 Radial Functions
    5. 6.8 General Solution for Interior Problems
    6. 6.9 Transient Radiation - Exterior Problems
    7. 6.10 Scattering from Spheres
    8. Problems
  13. Chapter 7: Spherical Nearfield Acoustical Holography
    1. 7.1 Introduction
    2. 7.2 Formulation of the Inverse Problem - Exterior Domain
    3. 7.3 Interior NAH
    4. 7.4 Scattering Nearfield Holography
    5. Problems
  14. Chapter 8: Green Functions and the Helmholtz Integral Equation
    1. 8.1 Introduction
    2. 8.2 Green’s Theorem
    3. 8.3 The Interior Helmholtz Integral Equation
    4. 8.4 Helmholtz Integral Equation for Radiation Problems (Exterior Domain)
    5. 8.5 Helmholtz Integral Equation for Scattering Problems
    6. 8.6 Green Functions and the Inhomogeneous Wave Equation
    7. 8.7 Simple Source Formulation
    8. 8.8 The Dirichlet and Neumann Green Functions
    9. 8.9 Construction of Interior Neumann and Dirichlet Green Functions by Eigenfunction Expansion
    10. 8.10 Evanescent Neumann and Dirichlet Green Functions
    11. 8.11 Arbitrarily Shaped Bodies and the Neumann Green Function
    12. 8.12 Conformal NAH for Arbitrary Geometry
    13. Problems
  15. Index

Product information

  • Title: Fourier Acoustics
  • Author(s): Earl G. Williams
  • Release date: June 1999
  • Publisher(s): Academic Press
  • ISBN: 9780080506906