Acoustics deals with the production, control, transmission, reception, and effects of sound. Owing to acoustics being an interdisciplinary field, this book is intended to be equally accessible to readers from a range of backgrounds including electrical engineering, physics and mechanical engineering.This book introduces the fundamentals of acoustic wave motion. It addresses in a clear and systematic way some of the most difficult parts of acoustics for beginners, such as the widely different approximations due to the wide frequency range, the apparently arbitrary choice between the use of analytical solutions to the wave equation with boundary conditions, and the fundamentally different energy-based considerations used in noise control. As a result, it provides readers with a self-contained source of information on acoustics which can be used for self-study or as a graduate course text.Key features:* Places an emphasis on detailed derivations based on the fundamental laws of physics and interpretations of the resulting formulas.* Avoids, where possible, electrical and mechanical equivalent circuits, so as to make it accessible to readers with different backgrounds.* Introduces duct acoustics, sound in enclosures, and sound radiation and scattering.* Contains a set of appendices which includes material on signal analysis and processing as these tools are essential for the modern acoustician.

About the Authors ixPreface xiList of Symbols xiii1 Introduction 12 Fundamentals of Acoustic Wave Motion 32.1 Fundamental Acoustic Concepts 32.2 The Wave Equation 53 Simple Sound Fields 113.1 Plane Waves 113.2 Sound Transmission Between Fluids 183.3 Simple Spherical Waves 224 Basic Acoustic Measurements 254.1 Introduction 254.2 Frequency Analysis 254.3 Levels and Decibels 294.4 Noise Measurement Techniques and Instrumentation 325 The Concept of Impedance 415.1 Mechanical Impedance 415.2 Acoustic Impedance 435.3 Specific Impedance, Wave Impedance and Characteristic Impedance 466 Sound Energy, Sound Power, Sound Intensity and Sound Absorption 496.1 Introduction 496.2 Conservation of Sound Energy 506.3 Active and Reactive Intensity 556.4 Measurement of Sound Intensity 616.4.1 Errors Due to the Finite Difference Approximation 636.4.2 Errors Due to Scattering 646.4.3 Errors Due to Phase Mismatch 646.5 Applications of Sound Intensity 686.5.1 Sound Power Determination 686.5.2 Noise Source Identification and Visualisation of Sound Fields 706.5.3 Transmission Loss of Structures and Partitions 706.5.4 Measurement of the Emission Sound Pressure Level 716.6 Sound Absorption 717 Duct Acoustics 757.1 Introduction 757.2 Plane Waves in Ducts with Rigid Walls 757.2.1 The Sound Field in a Tube Terminated by an Arbitrary Impedance 757.2.2 Radiation of Sound from an Open-ended Tube 827.3 Sound Transmission Through Coupled Pipes 867.3.1 The Transmission Matrix 877.3.2 System Performance 927.3.3 Dissipative Silencers 977.4 Sound Propagation in Ducts with Mean Flow 997.5 Three-dimensional Waves in Ducts with Rigid Walls 1017.5.1 The Sound Field in a Duct with Rectangular Cross Section 1017.5.2 The Sound Field in a Duct with Circular Cross Section 1077.5.3 The Sound Field in a Duct with Arbitrary Cross-sectional Shape 1147.6 The Green's Function in a Semi-infinite Duct 1167.7 Sound Propagation in Ducts with Walls of Finite Impedance 1227.7.1 Ducts with Nearly Hard Walls 1237.7.2 Lined Ducts 1258 Sound in Enclosures 1278.1 Introduction 1278.2 The Modal Theory of Sound in Enclosures 1278.2.1 Eigenfrequencies and Mode Shapes 1288.2.2 The Modal Density 1328.2.3 The Green's Function in an Enclosure 1338.3 Statistical Room Acoustics 1378.3.1 The Perfectly Diffuse Sound Field 1398.3.2 The Sound Field in a Reverberation Room Driven with a Pure Tone 1428.3.3 Frequency Averaging 1478.3.4 The Sound Power Emitted by a Point Source in a Lightly Damped Room 1488.4 The Decay of Sound in a Lightly Damped Room 1518.4.1 The Modal Approach to Decay of Sound 1518.4.2 The Statistical Approach to Decay of Sound 1548.5 Applications of Reverberation Rooms 1558.5.1 Sound Power Determination 1558.5.2 Measurement of Sound Absorption 1568.5.3 Measurement of Transmission Loss 1569 Sound Radiation and Scattering 1599.1 Introduction 1599.2 Point Sources 1599.2.1 Reciprocity 1659.2.2 Sound Power Interaction of Coherent Sources 1669.2.3 Fundamentals of Beamforming 1699.3 Cylindrical Waves 1719.3.1 Radiation from Cylindrical Sources 1719.3.2 Scattering by Cylinders 1839.4 Spherical Waves 1879.4.1 Radiation from Spherical Sources 1879.4.2 Scattering by Spheres 1999.4.3 Ambisonics 2019.5 Plane Sources 2029.5.1 The Rayleigh Integral 2039.5.2 The Wavenumber Approach 2079.5.3 Fundamentals of Near Field Acoustic Holography 2119.6 The Kirchhoff-Helmholtz Integral Equation 213Appendix A Complex Representation of Harmonic Functions of Time 217Appendix B Signal Analysis and Processing 221B.1 Introduction 221B.2 Classification of Signals 221B.3 Transient Signals 222B.3.1 The Fourier Transform 223B.3.2 Time Windows 229B.4 Periodic Signals 230B.4.1 Fourier Series 230B.4.2 The Fourier Transform of a Periodic Signal 232B.4.3 Estimation of the Spectrum of a Periodic Signal 234B.5 Random Signals 235B.5.1 Autocorrelation Functions and Power Spectra 237B.5.2 Cross-correlation Functions and Cross-power Spectra 239B.5.3 Estimation of Correlation Functions and Power Spectra 241B.6 Linear Systems 243B.6.1 Impulse Response and Frequency Response 244B.6.2 Estimation of the Frequency Response of a Linear System 248B.6.3 Estimation of the Frequency Response of a Weakly Nonlinear System 254B.7 Digital Signal Processing 255B.7.1 Sampling 255B.7.2 The Discrete Fourier Transform 256B.7.3 Signal Analysis with the 'Fast Fourier Transform' (FFT) 257B.7.4 The Method Based on 'Maximum Length Sequences' (MLS) 260Appendix C Cylindrical and Spherical Bessel Functions; Legendre Functions; and Expansion Coefficients 263C.1 Cylindrical Bessel Functions 263C.2 Legendre Functions 265C.3 Spherical Bessel Functions 266C.4 Expansion Coefficients 267Appendix D Fundamentals of Probability and Random Variables 269D.1 Random Variables 269D.2 The Central Limit Theorem 270D.3 Chi and Chi-Square Statistics 270Reference 271Bibliography 273Index 275