Pulse Propagation in Inhomogeneous Media

[+] Author and Article Information
D. B. Longcope

Sandia Laboratories, Albuquerque, New Mex.

C. R. Steele

Department of Aeronautics and Astronautics, Stanford University, Stanford, Calif.

J. Appl. Mech 41(4), 1057-1062 (Dec 01, 1974) (6 pages) doi:10.1115/1.3423433 History: Received December 01, 1973; Revised March 01, 1974; Online July 12, 2010


Approximate solutions are developed for one-dimensional pulse propagation in a medium with an analytic wave speed when the ratio ε of the pulse length to a characteristic length of the wave speed variation is small. The solutions describe an 0(1) transmitted pulse, given by the WKB solution, and an 0(ε) reflection which may progress in the opposite direction. Two approximations for the reflection are given, one in terms of explicit integrals and the other, which may be uniformly valid, by a combination of explicit integrals and a slowly varying numerical term. Comparisons with the exact solution in several examples show the usefulness of the approximate solutions.

Copyright © 1974 by ASME
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