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

## 2aSA10. Acoustical scattering by a penetrable wedge.

**Anthony M. J. Davis
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*Dept. of Math., Univ. of Alabama, Tuscaloosa, AL 35487-0350
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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.