Fundamental Physics of Ultrasound

395 Pages·1988·17.21 MB·\395

by  Shutilov (Author)

FUNDAMENTAL
PHYSICS OF
ULTRASOUND

FUNDAMENTAL
PHYSICS OF
ULTRASOUND
By
V.A. Shutilov
Translated from the Russian by
Michael E. Alferieff
/O\ CRC Press
\CE** 1 Taylor & Francis Group
^—-.*/ Boca Raton London New York
CRC Press is an imprint of the
Taylor & Francis Group, an informa business
Original version published in Russian in 1980 as Osnovy fiziki ul'trazvuka
by Leningrad University Press
Published 1988 by Gordon and Breach Science Publishers
Published 2020 by CRC Press
Taylor & Francis Group
6000 Broken Sound Parkway NW, Suite 300
Boca Raton, FL 33487-2742
© 1988 by Taylor & Francis Group, LLC
CRC Press is an imprint of Taylor & Francis Group, an Informa business
No claim to original U.S. Government works
ISBN-13: 978-2-88124-684-5 (pbk)
ISBN-13: 978-1-138-40425-0 (hbk)
This book contains information obtained from authentic and highly regarded sources. Reasonable
efforts have been made to publish reliable data and information, but the author and publisher cannot
assume responsibility for the validity of all materials or the consequences of their use. The authors and
publishers have attempted to trace the copyright holders of all material reproduced in this publication
and apologize to copyright holders if permission to publish in this form has not been obtained. If any
copyright material has not been acknowledged please write and let us know so we may rectify in any
future reprint.
Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced,
transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or
hereafter invented, including photocopying, microfilming, and recording, or in any information
storage or retrieval system, without written permission from the publishers.
For permission to photocopy or use material electronically from this work, please access
www.copyright.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc.
(CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit
organization that provides licenses and registration for a variety of users. For organizations that have
been granted a photocopy license by the CCC, a separate system of payment has been arranged.
Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are
used only for identification and explanation without intent to infringe.
Visit the Taylor & Francis Web site at
http ://www. taylorandfrancis.com
and the CRC Press Web site at
http://www.crcpress.com
Library of Congress Cataloging in Publication Data
Main entry under title:
Shutilov, Vladimir Aleksandrovich.
Fundamental physics of ultrasound.
Translation of: Osnovy fiziki ul'trazvuka.
Bibliography: p.
Includes index.
1. Ultrasonics. I. Title.
QC244.S4713 1988 534.5'5 87-21081
ISBN 2-88124-684-2
Contents
Foreword to the English Edition ix
Preface xi
List of Symbols xvi
I. BASIC EQUATIONS OF THE THEORY OF ELASTICITY
1. Description of the equilibrium and deformed states of a body 1
2. The stress tensor 9
3. Equation of motion 13
4. Relation between stress and strain. Generalized Hooke's Law 16
5. Energy of elastic deformation 20
6. The simplest deformations and the relation between the
different elastic moduli 23
II. PROPAGATION OF ULTRASONIC WAVES IN LIQUIDS
AND GASES
1. Acoustic properties of ideal liquids 28
2. The equations of hydrodynamics 30
3. Equation of state for liquids and gases 33
4. The wave equation 38
5. Plane waves 39
6. The velocity of sound 41
III. SINUSOIDAL PLANE WAVES WITH INFINITESIMAL
AMPLITUDE
1. Equation of a monochromatic plane wave 47
2. Basic linear relations between the physical quantities varying in
an ultrasonic wave. Characteristic impedance and acoustic
impedance 49
3. Energy characteristics of the ultrasonic field. Ultrasonic
intensity 54
NUMERICAL EXAMPLES. THE LOGARITHMIC
SCALE OF INTENSITIES AND AMPLITUDES 58
4. Absorption of monochromatic ultrasonic waves 60
5. Shear waves in liquids. Viscous losses at the boundaries of
ultrasonic beams 71
v
vi CONTENTS
IV. FINITE-AMPLITUDE PLANE WAVES
1. Estimation of the nonlinear terms in the equations of
hydrodynamics 77
2. The exact solution of the system of nonlinear equations of
hydrodynamics for a nondissipative medium 80
3. The velocity of propagation of a finite-amplitude wave.
Nonlinear properties of the medium 81
4. Relationship between the acoustic parameters in the second
approximation 87
5. Distortion of the form of a finite-amplitude wave during
propagation 88
6. Spectral analysis of a finite-amplitude wave 95
7. Intensity of distorted finite-amplitude ultrasonic waves 101
8. Absorption of finite-amplitude plane waves 103
V. STEADY FORCES ARISING IN AN ULTRASONIC FIELD
1. Radiation pressure 125
2. Radiation pressure forces on an obstacle 131
3. Steady forces acting on suspended particles in an ultrasonic field 137
4. Streaming 142
VI. ULTRASONIC CAVITATION
1. Rupture strength of liquids 149
2. Cavitation strength of a liquid 151
3. Collapse of a cavitation cavity 157
4. Dynamics of a cavitation cavity in an ultrasonic wave 163
5. Acoustic properties of a cavitating liquid 168
VII. REFLECTION, REFRACTION AND SCATTERING OF
ULTRASONIC WAVES
1. Transmission and reflection of plane waves at normal incidence
on the boundary between two media 172
2. Standing plane waves 180
3. Interference of oppositely traveling waves with normal
reflection in an absorbing medium 185
4. Reflection and refraction of a plane wave at oblique incidence
on a plane boundary between two media 188
5. Interference of plane waves at oblique incidence.
Quasistanding waves 195
6. Scattering of ultrasonic waves in an inhomogeneous medium 198
VIII. TRANSMISSION OF PLANE WAVES THROUGH LAYERS.
ELECTRO ACOUSTICAL ANALOGIES.
RADIATION OF PLANE WAVES
1. Transmission of ultrasonic plane waves through a plane-
parallel layer 211
CONTENTS vii
2. "Antireflection" (impedance-matched) layers 217
3. Characteristic acoustic oscillations of plates 223
4. Method of electroacoustical analogies 226
5. Oscillatory systems without damping 228
6. Characteristic oscillations of electric, mechanical and acoustic
oscillatory systems with damping 231
7. Forced oscillations. Resonance 237
8. Radiation of plane waves. The field of a real plane ultrasonic
radiator 244
IX. SPHERICAL WAVES
1. Wave equation for spherical waves 250
2. Monochromatic spherical waves 251
3. The intensity of a spherical wave 253
4. Radiation of spherical waves from a pulsating sphere 255
X. PROPAGATION OF ULTRASOUND IN AN ISOTROPIC
SOLID
1. Wave equation for an infinite solid 260
2. Reflection, refraction and transformation of ultrasonic waves
at the boundaries of solids 266
3. Reflection coefficient at the boundary of a solid at oblique
incidence 271
4. Rayleigh waves 285
5. Love waves 288
6. Geometric dispersion of sound in rods 291
7. Nonlinear elasticity and the origin of the nonlinear acoustics of
solids 295
XI. PROPAGATION OF ULTRASOUND IN CRYSTALS
1. General acoustic equations for crystals 300
2. Relationship between the elastic moduli and the velocities of
propagation of ultrasound in crystals 304
3. Cubic crystals 306
4. Crystals with lower symmetry 318
5. Influence of the piezoelectric effect on the elastic properties of
crystals 335
PROBLEMS AND THEIR SOLUTIONS
Problems 341
Solutions 347
REFERENCES 363
BIBLIOGRAPHY 371
SUBJECT INDEX 373

Foreword to the English edition
At the initiative of the publishers, the English translation of "Fundamental
Physics of Ultrasound" has been enhanced by the addition of problems and
their solutions for each chapter, inserted at the end of the book. These
additions should contribute toward a better understanding of the material,
and help the reader to go beyond the limits of the book. A bibliography of
monographs and manuals on ultrasonic physics has also been added.
Because of the untimely death of Professor V A Shutilov I have provided
these supplements.
DOCTOR E. V. TCHARNAYA.
IX