By
Avital Kaufman, Department of Geophysics, Colorado School of Mines, Golden, CO, USA
A.L. Levshin, Department of Physics, University of Colorado, Boulder, CO 80390, USA
Description
This book is dedicated to basic physical principles of the propagation of
acoustic and elastic waves. It consists of two volumes. The
first volume
includes 8 chapters and extended Appendices explaining mathematical aspects
of discussed problems. The first chapter is
devoted to Newton's laws, which,
along with Hooke's law, govern the behavior of acoustic and elastic waves.
Basic concepts of mechanics
are used in deriving equations which describe
wave phenomena. The second and third chapters deal with free and forced
vibrations as
well as wave propagation in one dimension along the system of
elementary masses and springs which emulates the simplest elastic medium.
In addition, shear waves propagation along a finite and infinite
string are discussed.
In chapter 4 the system of equations describing
compressional waves is derived.
The concepts of the density of the energy carried by waves, the energy flux, and
the Poynting vector
are introduced. Chapter 5 is dedicated to propagation of
spherical, cylindrical, and plane waves in homogeneous media, both in time and
frequency domains. Chapter 6 deals with interference and diffraction. The
treatment is based on Helmholtz and Kirchhoff formulae. The
detailed discussion
of Fresnel's and Huygens's principles is presented. In Chapter 7 the effects of interference of waves with close
wave numbers and frequencies are considered. Concepts such as the wave group, the group velocity, and
the stationary phase important
for understanding propagation of dispersive waves are introduced.
The final chapter of the first volume is devoted to the principles
of
geometrical acoustics in inhomogeneous media.
Included in series
Methods in Geochemistry and Geophysics
