Understanding Plane Waves

233 Pages·2020·8.371 MB·English

by  William A. Cooper (editor)

PHYSICS RESEARCH AND TECHNOLOGY

UNDERSTANDING PLANE WAVES

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PHYSICS RESEARCH AND TECHNOLOGY

UNDERSTANDING PLANE WAVES

WILLIAM A. COOPER
EDITOR
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ISBN: (cid:28)(cid:26)(cid:27)(cid:16)(cid:20)(cid:16)(cid:24)(cid:22)(cid:25)(cid:20)(cid:25)(cid:16)(cid:27)(cid:21)(cid:21)(cid:16)(cid:27)(cid:3)(cid:11)(cid:72)(cid:69)(cid:82)(cid:82)(cid:78)(cid:12)

Published by Nova Science Publishers, Inc. † New York
CONTENTS

Preface vii
Chapter 1 Recent Progress in Acoustical Theory
and Applications 1
Lin Fa and Meishan Zhao
Chapter 2 Recent Development of an
Acoustic Measurement System 113
Lin Fa and Meishan Zhao
Chapter 3 Plane Nonlinear Elastic Waves:
Approximate Approaches to Analysis of Evolution 147
Jeremiah Rushchitsky
Chapter 4 Spacetime Symmetries and Interaction of
Quantum Relativistic Particles with
External Plane Wave Fields 203
H. K. Ould-Lahoucine
Index 217
Related Nova Publications 221

PREFACE

As a critical theoretical advance, Understanding Plane Waves
discusses the acoustic Goos-Hänchen effect. The important applications of
this effect are discussed, including plane wave propagating inside
transversely isotropic elastic-solids, reflection/refraction at interface
between two anisotropic rocks, and acoustical applications to petroleum
logging and seismic exploration.
Next, the authors explore a newly developed acoustic-measurement
system with emphasis on measurement process and recent improvements
that make an acoustic-measurement more accurate.
Three approaches which are used to analyze the evolution of the plane
longitudinal and transverse waves that are propagated in a nonlinear
hyperelastic medium are discussed: the method of successive
approximations, the method of slowly varying amplitudes and the method
of restriction on the displacement gradient.
Lastly, the subject of relativistic quantum particles interacting with
classical plane wave fields is examined from the standpoint of space-time
symmetries which have been found to be encoded in the solutions of
relativistic equations.
Chapter 1 - Studies of plane wave propagating inside applied media
have been central to the development of our understanding of acoustics, so
as to the development of applied technologies. It was understood from the
viii William A. Cooper
beginning of these studies that a detailed description of plane wave
propagating inside anisotropic media is extremely important. Recent
research progress in this aspect has attracted the attention of scientists from
both the physical sciences and the biological sciences divisions. In this
chapter, the authors begin with introducing some basic but important
concepts of plane wave propagating inside isotropic/anisotropic media,
including electric-acoustic conversions, elliptical-polarization states,
anisotropy effect on time-depth relation, and more. As a critical theoretical
advance, the authors will discuss the acoustic Goos-Hänchen effect. The
important applications will be discussed, including plane wave propagating
inside transversely isotropic elastic-solids, reflection/refraction at the
interface between two anisotropic rocks, and acoustical application to
petroleum logging and seismic exploration, e.g., slim-hole acoustic-
logging tool, conversions of acoustic logging signal, as well as seismic
signal and data analysis. The authors end the chapter with some concluding
remarks and speculations.
Chapter 2 - The authors discuss a newly developed acoustic-
measurement system with emphasis on measurement process and recent
improvements that make an acoustic-measurement more accurate. This
system is based on a model electric-acoustic transmission-network which
consists of a series of parallel-connected equivalent-circuits. For acoustic-
transducers, the authors place special emphasis on the importance of the
contribution from each individual frequency component of an excitation
signal, the propagation medium, and the cumulative signal-output from
transducer’s mechanic/electric terminals. The system has been tested for
realistic acoustic transmission. Based on the results of the measurement,
the authors conclude that this system is easy to operate, user friendly, and
highly accurate.
Chapter 3 - Three approaches (methods) are used to analyze the

evolution of the plane longitudinal and transverse waves that are
propagated in a nonlinear hyperelastic medium - method of successive

approximations,methodofslowlyvaryingamplitudes, method of restriction

on the displacement gradient. The evolution is understood in thestandard

forphysicsmeaning: thewavewithsomegiveninitialprofile(harmonic or
Preface ix
solitary) evolves, that is, changes this profile. The term “the profile is
distorted” is used sometimes too. Themedium of propagation is described

by the well-known in nonlinear mechanics of materials five-constant

Murnaghan model. First, the noted methods are described briefly as
applied to the wave propagation problems. Further, the longitudinal and
transverse plane waves are analyzed separately. The point is that the

Murnaghan model describes the longitudinal wave by the quadratic

nonlinear wave equation, whereas the transverse wave – by the cubic
nonlinear wave equation. Ten variants (known and new = published and
unpublished) for the longitudinal wave and four variants for the transverse
wave (known and new = published and unpublished) of an approximate
analysis are described and commented on. It is shown that each variant
provides an answer on a certain aspect in the initial wave profile evolution
study. A statement of some variants is accompanied by the 2Dand 3D

pictures.Anattention is drawn tothefeatures of the evolutionprocess as

well as to similarities and differences in the results obtained.
Chapter 4 - The subject of relativistic quantum particles interacting
with classical plane wave fields is examined from the standpoint of the
space-time symmetries which have been found to be encoded in the
solutions of relativistic equations. Principally, it is shown how the elements
of the proper Lorentz group come into play as a basic ingredient to get the
solution of the Dirac equation under the form of variable transformations
acting on the free-field solution. Subsequently, this underlying Lorentz
structure is also found in the full solutions of spin 1 particles in interaction
with classical plane wave fields by mean of a local gauge, a Lorentz and
displacement transformations (ULT) acting as variable transformations on
the free-field. On the other hand, considering the role played by the
relativistic Green function as a fundamental object in the description of
several scattering processes in quantum electrodynamics (QED) involved
with the electromagnetic plane waves, an exhaustive review is done of the
different approaches devoted to its derivation including the algebraic
methods, path integrals and worldline formalisms.