Fundamentals of General Linear Acoustics

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.

Finn Jacobsen, Department of Electrical Engineering, Technical University of Denmark (DTU)
Currently an Associate Professor in the Department of Electrical Engineering at DTU, Dr. Jacobsen has more than twenty-five years’ experience of teaching acoustics at MSc level, and more than 15 years’ experience of teaching fundamentals of acoustics at undergraduate level. He was Associate Editor of Acustica united with Acta Acustica from 1995 to 2003, and section leader of the Handbook of Signal Processing in Acoustics (Springer, 2008). He has also contributed 6 chapters in various handbooks on acoustics; published approx. 90 journal papers and more than 100 conference papers.

Peter Møller Juhl, Faculty of Engineering, University of Southern Denmark
Dr. Juhl is currently an Associate Professor at the Institute of Technology and Innovation, University of Southern Denmark. He teaches both undergraduate and postgraduate courses in the field of acoustics which range from quite elementary acoustics and signal analysis for students of audiology to basic and advanced acoustics for engineering students as well as courses on mechanical vibrations and numerical acoustics. He has also taught basic courses on physics for both engineers and physicists.

Preface

List of symbols

1 Introduction

2 Fundamentals of Acoustic Wave Motion

2.1 Fundamental acoustic concepts

2.2 The wave equation

References

3 Simple Sound Fields

3.1 Plane waves

3.2 Sound transmission between fluids

3.3 Simple spherical waves

References

4 Basic Acoustic Measurements

4.1 Introduction

4.2 Frequency analysis

4.3 Levels and decibels

4.4 Noise measurement techniques and instrumentation

References

5 The Concept of Impedance

5.1 Mechanical impedance

5.2 Acoustic impedance

5.3 Specific impedance, wave impedance and characteristic impedance

References

6 Sound Energy, Sound Power, Sound Intensity and Sound Absorption

6.1 Introduction

6.2 Conservation of sound energy

6.3 Active and reactive sound intensity

6.4 Measurement of sound intensity

6.4.1 Errors due to the finite difference approximation

6.4.2 Errors due to scattering

6.4.3 Errors due to phase mismatch

6.5 Applications of sound intensity

6.5.1 Sound power determination

6.5.2 Noise source identification and visualisation of sound fields

6.5.3 Transmission loss of structures and partitions

6.5.4 Measurement of emission sound pressure level

6.6 Sound absorption

References

7 Duct Acoustics

7.1 Introduction

7.2 Plane waves in ducts with rigid walls

7.2.1 The sound field in a duct terminated by an arbitrary impedance

7.2.2 Radiation of sound from an open-ended tube

7.3 Sound transmission through coupled pipes

7.3.1 The transmission matrix

7.3.2 System performance

7.3.3 Dissipative silencers

7.4 Propagation of plane waves in ducts with mean flow

7.5 Three-dimensional waves in ducts with rigid walls

7.5.1 The sound field in a duct with rectangular cross section

7.5.2 The sound field in a duct with circular cross section

7.5.3 The sound field in a duct with arbitrary cross-sectional shape

7.6 The Green’s function in a semi-infinite duct

7.7 Sound propagation in ducts with walls of finite impedance

7.7.1 Duct with nearly hard walls

7.7.2 Lined ducts

References

8 Sound in Enclosures

8.1 Introduction

8.2 The modal theory of sound in enclosures

8.2.1 Eigenfrequencies and mode shapes

8.2.2 The modal density

8.2.3 The Green’s function in an enclosure

8.3 Statistical room acoustics

8.3.1 The perfectly diffuse sound field

8.3.2 The sound field in a reverberation room driven with a pure tone

8.3.3 Frequency averaging 

8.3.4 The sound power emitted by a point source in a lightly damped room

8.4 The decay of sound in lightly damped rooms

8.4.1 The modal approach to decay of sound

8.4.2 The statistical approach to decay of sound

8.5 Applications of reverberation rooms

8.5.1 Sound power determination

8.5.2 Measurement of sound absorption

8.5.3 Measurement of transmission loss

References

9 Sound Radiation and Scattering

9.5 Introduction

9.5 Point sources

9.2.1 Reciprocity

9.2.2  Interaction of coherent sources

9.2.3 Fundamentals of beamforming

9.3 Cylindrical waves

9.3.1 Radiation from cylindrical sources

9.3.2  Scattering by cylinders

9.4 Spherical waves

9.4.1 Radiation from spherical sources

9.4.2 Scattering by spheres

9.4.3 Ambisonics

9.5 Plane sources

9.5.1 The Rayleigh integral

9.5.2 The wavenumber approach

9.5.3 Fundamentals of near field acoustic holography

9.6 The Kirchhoff-Helmholtz integral equation

References

Appendix A: Complex Representation of Harmonic Functions of Time

Appendix B: Signal Analysis and Processing

B.1 Introduction

B.2 Classification of signals

B.3 Transient signals

B.3.1 The Fourier transform

B.3.2 Time windows

B.4 Periodic signals

B.4.1 Fourier series

B.4.2 The Fourier transform of a periodic signal

B.4.3 Estimation of the spectrum of a periodic signal

B.5 Random signals

B.5.1 Autocorrelation functions and power spectra

B.5.2 Cross-correlation functions and cross-power spectra

B.5.3 Estimation of correlation functions and power spectra

B.5 Linear systems

B.6.1 Impulse response and frequency response

B.6.2 Estimation of the frequency response of a linear system

B.6.3 Estimation of the frequency response of a weakly nonlinear system

B.7 Fundamentals of digital signal processing

B.7.1 Sampling

B.7.2 The discrete Fourier transform

B.7.3 Signal analysis with the ‘Fast Fourier Transform’(FFT)

B.7.4 The method based on ‘Maximum Length Sequencies’ (MML)

References

Appendix C: Cylindrical and Spherical Bessel Functions; Legendre Functions; and Expansion Coefficients

C.1 Cylindrical Bessel functions

C.2 Spherical Bessel functions

C.3 Legendre functions

C.4 Expansion coefficients

References

Appendix D: Fundamentals of Probability and Random Variables

D.1 Random variables

D.2 The central limit theorem

D.3 Chi and Chi-square statistics

References

Bibliography

Index

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