Y. L. Li
Dept. of Elec. and Comput. Eng., Univ. of Illinois at Urbana--Champaign, Rm. 60G Everitt Lab., 1406 W. Green St., Urbana, IL 61801
Michael J. White
US Army Construction Eng. Res. Lab.
M. H. Hwang
Univ. of Illinois at Urbana--Champaign, Urbana, IL 61801
The problem of sound reflection of a spherical wave from a locally reacting surface is studied by a new method, which is based on the solution of the heat equation. The new method maps the wave equation formulation with its associated boundary condition to a heat equation problem. In the heat equation domain, a Green's function solution is relatively easy to obtain via the inverse Laplace transform. Finally, a compact approximation of the Green's function for a point source above an impedance ground has been obtained using the method of stationary phase. Numerical comparisons show that the new expression is often more accurate than those obtained by more complicated techniques, such as the method of steepest descent. Following the same procedures, a new expression of the Green's function for a horizontal line acoustic source above an impedance ground is also given.