Acoustical Radiation from a Point Source in the Presence of Two Media

Abstract

Two semi-infinite isotropic media (porous or nonporous) are separated by a plane interface. A simple point source of sound is imbedded in either of the media. Expressions for the resultant wave function are obtained by the method of steepest descents as modified by Banos and Wesley. In particular, two different asymptotic solutions are presented. The first solution is valid in the vicinity of the interface. The expansions, calculated out to three terms, yield the wave solution as a continuous function of the parameters of the two media and the space coordinates for horizontal ranges beginning at small distances from the source and extending to infinity. It is shown that a surface wave exists and that this wave gradually disappears when the horizontal range becomes sufficiently large. The second solution consists of a simple three term asymptotic expansion valid in the vicinity of the vertical axis. The mathematical treatment uses a new path of integration not found in the literature on this problem.