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
- Cover image
- Title page
- Table of Contents
- Dedication
- Copyright
- Preface
- Chapter 1: Fourier Transforms & Special Functions
-
Chapter 2: Plane Waves
- 2.1 Introduction
- 2.2 The Wave Equation and Euler’s Equation
- 2.3 Instantaneous Acoustic Intensity
- 2.4 Steady State
- 2.5 Time Averaged Acoustic Intensity
- 2.6 Plane Wave Expansion
- 2.7 Infinite Plate Vibrating in a Normal Mode
- 2.8 Wavenumber Space: k-space
- 2.9 The Angular Spectrum: Fourier Acoustics
- 2.10 Derivation of Rayleigh’s Integrals
- 2.11 Farfield Radiation: Planar Sources
- 2.12 Radiated Power
- 2.13 Vibration and Radiation from an Infinite Point-driven Plate
- 2.14 Vibration and Radiation of a Finite, Simply Supported Plate
- 2.15 Supersonic Intensity
- Problems
-
Chapter 3: The Inverse Problem: Planar Nearfield Acoustical Holography
- 3.1 Introduction
- 3.2 Overview of the Theory
- 3.3 Presentation of Theory for a One-Dimensional Radiator
- 3.4 Ill Conditioning Due to Measurement Noise
- 3.5 The k-space Filter
- 3.5.1 Examples
- 3.6 Modification of the Filter Shape
- 3.7 Measurement Noise and the Standoff Distance
- 3.8 Determination of the Cutoff Frequency for the k-space Filter
- 3.9 Finite Measurement Aperture Effects
- 3.10 Discretization and Aliasing
- 3.11 Use of the DFT to Solve the Holography Equation
- 3.12 Reconstruction of Other Quantities
- 3.12.1 Time Domain
- Problems
- Chapter 4: Cylindrical Waves
- Chapter 5: The Inverse Problem: Cylindrical NAH
- Chapter 6: Spherical Waves
- Chapter 7: Spherical Nearfield Acoustical Holography
-
Chapter 8: Green Functions and the Helmholtz Integral Equation
- 8.1 Introduction
- 8.2 Green’s Theorem
- 8.3 The Interior Helmholtz Integral Equation
- 8.4 Helmholtz Integral Equation for Radiation Problems (Exterior Domain)
- 8.5 Helmholtz Integral Equation for Scattering Problems
- 8.6 Green Functions and the Inhomogeneous Wave Equation
- 8.7 Simple Source Formulation
- 8.8 The Dirichlet and Neumann Green Functions
- 8.9 Construction of Interior Neumann and Dirichlet Green Functions by Eigenfunction Expansion
- 8.10 Evanescent Neumann and Dirichlet Green Functions
- 8.11 Arbitrarily Shaped Bodies and the Neumann Green Function
- 8.12 Conformal NAH for Arbitrary Geometry
- Problems
- Index
Product information
- Title: Fourier Acoustics
- Author(s):
- Release date: June 1999
- Publisher(s): Academic Press
- ISBN: 9780080506906
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