## Theodor F. Hueter and Richard H. Bolt

Published in 2000; Originally Published in 1954

### CONTENTS

Preface to the Original Edition

Chapter 1 INTRODUCTION

1.1 A Definition of Sonics
1.2 Frequency Limits
1.3 Scope of Applications
1.4 The Choice of Units; the MKS System
Chapter 2 BASIC PRINCIPLES

2.1 Fundamentals of Vibration
2.2 The Equations of Motion
2.3 A Solution by Electric Circuit Analogy; Mechanical Impedance
2.4 General Behavior of Driven Damped Oscillator
2.5 Some Properties of Wave Motion
2.6 Velocity of Waves on a String
2.7 Vibrations in Solids
2.8 Sound Waves in Fluids
2.9 Acoustic Impedance and Plane-Wave Transmission
2.10 Pressure Reflectivity and Transmissivity
2.11 Energy, Intensity, and Power
2.12 Radiation Pressure
2.13 The Decibel Notation
Chapter 3 RADIATION

3.1 Spherical Waves
3.2 Radiation Impedance
3.3 Directivity; the Far Field
3.4 The Near Field (Fresnel Diffraction)
3.5 Coincidence Principle: Refraction, Reflection, and Transmission
3.6 The Doppler Effect
3.7 Scattering
Chapter 4 PIEZOELECTIRC TRANSDUCERS

4.1 General Aspects of Electric Field Drive
4.2 Piezoelectric Properties
4.3 Fundamentals of Piezoelectric Transduction
4.4 Simple Theory of Equivalent Circuits for Transmitters
4.5 Power Conversion and Matching
4.6 The Q of Transducers
4.7 Resonance and Antiresonance
4.8 The Electromechanical Coupling Factor
4.9 Determination of Transducer Efficiency from the Circle Diagram
4.10 Piezoelectric Response of Common Transducer Materials
4.12 Simple Theory of Piezoelectric Receivers
4.13 Multiple-Layer Transducers
4.14 Non-Directional Cylindrical Receivers
4.15 Vibration Pick-ups
4.16 General Electroacoustic Relationships
Chapter 5 MAGNETROSTRICTIVE TRANSDUCERS

5.1 General Concept of Magnetic Coupling
5.2 Phase Relationships in Magnetic Transduction
5.3 Magnetostrictive Properties
5.4 Eddy Currents and Hysteresis
5.5 The Motional Impedance Loop
5.6 Efficiency and Matching
5.7 Design Considerations for Laminated Stacks
5.8 Determination of Equivalent Lumped Constants
5.9 Some Practical Aspects of Magnetrostrictive Transducers
Chapter 6 PHYSICAL MECHANISMS FOR SONIC PROCESSING

6.1 General Considerations
6.2 Sound Fields in Processing Tanks
6.3 Fundamentals of Gas Kinetics
6.4 Relative Velocity Effects; Particle Agglomeration
6.5 Large-Amplitude Effects in Gases
6.6 Steady Sonic Forces on Particles in a Fluid
6.7 Basic Aspects of Cavitation in Liquids
6.8 Factors Determining the Threshold of Cavitation
6.9 Processing by Cavitation
Chapter 7 DEVICES AND TECHNIQUES FOR SONIC PROCESSING

7.1 Criteria for Transducer Selection
7.2 Special Properties of Barium Titanate
7.3 Principles of Ultrasonic Applicator Design
7.4 Focusing Systems
7.5 Sound Conduction through Solid Rods
7.6 Electrodynamic Vibrators
7.7 Fluid Dynamic Systems
7.8 Sonic Siren Generators
7.9 Sonic Oscillators Operated by Hydrodynamic Valve Action
7.10 Special Mechanical Transducers for Low Frequencies
Chapter 8 PRINCIPLES OF SONIC TESTING AND ANALYSIS

8.1 The Rationale of Sonic Measurements
8.2 Resonance Techniques
8.3 Optical Analysis of Standing Waves
8.4 Interferometric Techniques
8.5 Continuous Wave Propagation Techniques
8.6 Electric Impedance Methods
8.7 Decay and Reverberation Techniques
8.8 Internal Damping in Metals
8.9 Complex Wave Forms and Transient Pulses
8.10 Ultrasonic Pulse Techniques
Appendix ACOUSTICAL RELAXATION MECHANISMS IN FLUIDS

A.1 General Relations between Macroscopic and Microscopic Properties
A.2 Phase Lag between Pressure and Density
A.3 Classical Absorption and Velocity Dispersion
A.4 Molecular Relaxation in Gases
A.5 Structural Aspects of Sound Propagation in Liquids
A.6 Sound Propagation in Fluid Mixtures and Solutions
Author Index

Subject Index

**Preface to the Original Edition**

During the past few years we have received many inquiries regarding industrial uses of sound
and ultrasound: metals testing, spot welding, drilling, gas analysis, medical diagnosis, aerosol
agglomeration, fish location, clothes washing, degreasing--these and many other real or
imaginary uses of sound have come up for discussion. In trying to solve some of these problems
and in studying the expanding literature on these seemingly unrelated subjects, we began to see
that to see that a new area of technology was taking shape. The multiplicity of concepts and
techniques could be designated by the name *sonics*, much as electronics and nucleonics
connote particular areas of technical practice.

*Sonics* encompasses the analysis, testing, and processing of materials and products by the
use of
mechanical vibratory energy. The particular frequency that is best suited for a given task is
determined by the special requirements and limitations of that task. All applications, however,
are based on the same physical principals, and the relation of the frequency to the range of
audibility for man's ear is irrelevant from this point of view.

The unity of *sonics* is, therefore, the keynote of this book. The common principles are
presented
in general form and then applied in many special ways to the design of sonic techniques for a
particular medium or frequency range. The relevant fundamentals of vibration and sound are
given in Chapters 2 and 3, and general aspects of transducers for sound generation and reception
are presented in Chapters 4 and 5. The applications are divided into two branches: sonic
processing, Chapters 6 and 7; and sonic analysis, Chapter 8. Molecular aspects of sound
propagation in fluids, a topic of particular interest in modern physics, are discussed in the
Appendix following Chapter 8.

The wide diversity in the possible applications of sonics and in the professional backgrounds of
its potential users has posed our most challenging problem. A book that was understandable
only
to an advanced physicist would be of limited usefulness in many industrial developments. A
purely practical discussion of devices and design formulas would not provide an adequate basis
for the exploration of entirely new applications. We have tried to find a middle ground. The
underlying physics is presented as simply as possible, with plausibility arguments frequently
used
in place of rigorous derivations. The associated mathematical expressions are also given in
simple form, but in many cases the implications of a fuller mathematical treatment are pointed
out in a footnote or in small type, as in our discussion of the tensor notation for crystal
transducers.

Wherever possible a discussion is concluded with simplified engineering formulas and with
practical instructions for their use. We have deliberately not discussed, or even enumerated, all
of the applications that have been mentioned in the literature. Instead, typical examples have
been selected that illustrate the operating principles and that suggest other uses in many fields.
We have tried to make this book understandable to anyone with college training or its equivalent
in any branch of science or engineering. In particular, we have assumed that the reader has little
or no specialized training in acoustics, but that he has some understanding of electronics.

The bibliography and the references to collateral reading have been selected with particular care.
We have included only those that are most informative on a given subject or that give the most
recent review of earlier developments along a particular line. Extensive bibliographies, to more
that 5000 entries, are contained in other publications to which we refer.

Our attempts to systematize this subject started in 1950 when we prepared a series of lectures
which one of us (R.H.B.) delivered during successive weeks to the Shell Development Company,
San Francisco, and the California Research Corporation, L Habra, California. We are greatly
indebted to these two organizations for their encouragement in the starting of this book. In 1951
we gave a special summer session course, "Industrial Applications of Acoustics," at the
Massachusetts Institute of Technology. Stimulating discussions by the participants, who
represented many different industries, led to a considerable expansion of our subject matter. In
the spring of 1953 one of us (T.F.H.) initiated a full-term course in the Department of Physics at
Massachusetts Institute of Technology, using a large segment of this book for class notes.
Suggestions made by the students have helped us in the final reworking of the manuscript.

We are indebted to many colleagues and industrial organizations for making available much
interesting and timely information as noted in specific acknowledgments throughout the text.
We are grateful to S.J. Lukasik and M.S. Cohen for careful reading and assistance with some of
the material; to C. Twardzik for skillful drawing of the illustrations; and especially to F. Massa
for critical review and many helpful suggestions. We also express deepest appreciation to our
wives, whose complaints during out protracted period of writing lay strictly outside the audible
range.

T.F. Hueter

R.H. Bolt

Cambridge, Massachusetts

November, 1954

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