Preface to the Original Edition

Introduction

- The Nature of Nonlinear Acoustics
- Historical Aspects
- Aeroacoustics
- Shock Waves
- Finite-Amplitude Waves
- Interaction of Sound with Sound
- Radiation Pressure
- Streaming
- Cavitation

Principles of Linear Acoustics

- The Linear Oscillator
- The Vibrating String
- Beats
- Plane Waves, Nondissipative Case
- Spherical and Cylindrical Waves
- Sound Absorption
- Relaxation Phenomena
- Radiation Field of a Piston Source. Diffraction
- Refraction, Reflection and Scattering of Acoustic Waves
- Surface Waves
- Waves on a Liquid Surface
- Waves on a Solid Surface

Some Sources of Nonlinear Oscillations

- The Simple Pendulum
- Nonlinear Springs
- Undamped Forced Oscillations with Nonlinear
- Restoring Force
- Effect of Damping. Duffing's Equation
- Subharmonics
- Nonlinear Strings
- Nonlinearity in Membranes
- Nonlinearity of Plates
- Tartini Tones

Nonlinear Propagation in Fluids

- Formulation of the Wave Equations, Lagrangian and
- Eulerian Coordinates
- Earnshaw Solution of the Wave Equation. The Discontinuity Solution
- Riemann's Solution
- The Fubini Solution
- The Viscous Case. Perturbation Analysis
- Other Methods of Solution
- Burgers' Equation
- Blackstock's Bridging Function
- Work of Soluyan and Khokhlov
- Spherical and Cylindrical Waves of Finite Amplitude
- Case of a Relaxing Medium
- Experimental Verification
- Practical Sources of Finite Amplitude Sound
- Finite amplitude Propagation in Tubes

Shock Waves

- The Randine-Hugoniot Equation
- The Shock Tube
- Reflection of Shocks
- Method of Characteristics
- Shock Wave Structure
- Shock Thickness in Liquids
- N. Waves. The Sonic Boom
- Underwater Explosions

Aeroacoustics

- The Lighthill Equations
- Monopole, Dipole, Quadrupole Sources
- Sound from Changes in Vortex Strength
- Sound from Movement of Vorticity in Free Flow

Radiation Pressure

- The Rayleigh Radiation Pressure
- The Langevin Radiation Pressure
- Higher Order Effects
- Effect of Reflection
- Radiation Stress Tensor
- Interface between Two Nonmiscible Liquids
- Radiation Pressure Devices

Streaming

- Basic Equations
- Plane Waves in an Unbounded Medium
- Case of a Cylindrical Tube
- Experimental Studies
- Plane Wave Traveling between Parallel Walls
- Standing Waves between Parallel Walls
- Oscillatory Flow near a Cylinder
- Some Further Experimental Work

Cavitation

- The Nature of Cavitation
- Static Bubble Theory
- Dynamic Bubble Theory
- Experimental Evidence of Cavitation Thresholds
- Origin and Stability of Cavitation Nuclei
- Cavitation Noise
- Sonoluminescence

Nonlinear Interaction of Sound Waves

- Lighthill, Ingard, Westervelt (1950-1960)
- Dean, Lauvstad, Tjotta (1960-1966)
- Berktay, Al-Temimi
- Jones and Beyer
- Collinear Beams
- Absorption of Sound by Sound
- Scattering of Sound by Sound in the Presence of Obstacles
- Interaction of Pulses of Finite Amplitude

Applications of Nonlinear Interactions. The Parametric Array

- Far-field Transmission
- Near-field Transmission
- Far-field Receiving
- Near-field Receiving
- Other Applications of the Parametric Array
- Arrays of Parametric Arrays
- A Standing Wave Parametric Source (SWAPS)
- Nonlinear Interactions in Intense Noise

Nonlinear Propagation in Solids

- General Aspects
- Lattice Vibrations in Crystals. The Debye
- Approximation
- Nonlinear Lattice Waves
- Third Order Elastic Constants
- Ultrasonic Determination of Third Order Elastic Constants
- Interaction of Sound with Sound
- Nonlinear Surface Wave

APPENDIX

AUTHOR INDEX

SUBJECT INDEX

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The idea of writing this book occurred to the author one night while he was in the hospital, between surgical operations. Whether he was under sedation at the time, or whether the idea was an hallucination, is best left to the judgment of the reader.

The opportunity to write the book was provided by a sabbatical leave from Brown University, spent in the Department of Electrical and Electronic Engineering at the University of Birmingham (U.K.) in 1971, and the writer extends his thanks to the Department Head, Professor David Tucker, Dr. O.H. Berktay, for their help in making the stay both possible and fruitful. Particular acknowledgment must be made to the University and Department librarians at Birmingham for their courtesy and helpful service.

The finishing of a book requires the assistance and cooperation of many. Thanks are of course due to Brown University on many points. The writer is also grateful to his colleagues in the Department of Physics at Brown, especially Professors A.O. Williams, Jr. and Peter J. Westervelt, for conversations on acoustical problems that have assisted in the preparation of this book. Special thanks are due Professor Mark B. Moffett of the University of Rhode Island who, in the spirit of "once a graduate student, always a graduate student," reviewed a good fraction of the book in some detail. The book was supported by the Naval Sea Systems Command under Contract N00024-72-C-1397 with Brown University.

The author acknowledges with thanks the cooperation of Academic Press for allowing to use materials in this book from the author's previous publications with that company. Acknowledgment should also be made to various secretaries who worked on parts of the manuscript, with special thanks to Miss Maureen Byrne, who typed most of the text twice.

Finally, gratitude is due to my wife and family, for putting up once again with an author in the house.

Robert T. Beyer

February 14, 1974

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When this book first appeared, nonlinear acoustics had just reached a plateau of intense activity. Some of this was caught in the text, but a great deal of it came later and was unavoidably missed. This reprinting of the 1974 text (which actually appeared in 1976) provides an opportunity at least to note some of the developments since that time, and to supply a list of references, where the reader can follow the new developments in more detail. In order to avoid the expense of a major overhaul of the text, these additional comments and references are included as an Appendix.

The reprinting also provides an opportunity to make corrections of errata. The author is grateful to David T. Blackstock, who furnished him a list of such corrections many years ago, and to Ken Rolt, who recently supplied some additional ones. And there are a few that the author himself has found.

The author is also grateful to the late Francis H. Fenlon, who wrote a long and critical review of the text in JASA (61, 1395-1996(1977, with many useful suggestions, some of which are referred to in the Appendix). In addition, he thanks Professor I.I. Glass of the University of Toronto for making available material on shock waves that was only referenced second hand in the 1974 publication.

It should be noted that the preface of the original publication was dated 14 February 1974, the occasion of the author's thirtieth wedding anniversary. He is now delighted to renew the dedication of this book to his wife in this, the year of their Golden Wedding Anniversary.

Robert T. Beyer

March, 1994

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