Reflection of waves from a point source by an impedance boundary

Abstract

The problem of finding a solution of the scalar wavefield produced by a point source in the presence of an infinite ’’impedance’’ boundary is treated. The analysis is made with a method used by Ingard, which has been corrected. It is shown that it is possible to rewrite the exact solution in terms of a single integral along a steepest-descent contour and a Hankel function. Asymptotical expansions of the solution is in consistency with expansions by Wenzel, who found that in a special case expansions of his and Ingard’s solution differ by a ’’surface wave’’ term. The asymptotical expansions are given as examples. The main result, the single integral and the Hankel function, could easily be integrated numerically. Subject Classification: [43]28.40; [43]20.15, [43]20.30, [43]20.55.