11.—High-Frequency Scattering in a Certain Stratified Medium. The Two-part Problem

Abstract

SynopsisThe propagation of scalar waves in a certain two-dimensional medium is considered. The incident field, which is due to the presence of a line source, is scattered by two coupled half-planes on each of which the impedance takes a constant value. The Wiener-Hopf technique is used to find a solution which is then examined asymptotically for high frequency. It is found that there is an illuminated region in which the solution is expressed in terms of geometrical optics rays, and a shadow region in which the solution is described by creeping modes. The point of impedance discontinuity may be regarded as producing secondary radiation. The nature of this secondary radiation is quite different according as the point of impedance discontinuity lies in the illuminated or shadow region of the geometrical optics field produced by the source.