ASA 129th Meeting - Washington, DC - 1995 May 30 .. Jun 06

2aSA10. Acoustical scattering by a penetrable wedge.

Anthony M. J. Davis

Dept. of Math., Univ. of Alabama, Tuscaloosa, AL 35487-0350

Consider the two-dimensional scattering of a time-harmonic sound wave generated by a line source and incident upon a penetrable wedge. The wave speeds in the interior and exterior of the wedge are distinct and the radiation condition of only outgoing waves at infinity is applied in all directions. At the boundary of the wedge there is a pair of transmission conditions which ensure continuity of the acoustic pressure and normal velocity. By using suitably modified Green's functions and considering separately the symmetric and antisymmetric parts of the pressure field with respect to the center plane of the wedge, a pair of disjoint integral equations of the first kind can be obtained for the two parts of the normal velocity on just one face of the wedge. Transformation to equations of the second kind is then achieved by using a technique for solving integral equations with Hankel function kernels [D. Porter, IMA, J. Appl. Math. 33, 211--228 (1983)]. The new kernels are bounded but defined on the interval (0, (infinity)). A numerical solution must describe the far field which, at the wedge boundary, will exhibit some mixture of the two wave speeds.