### ASA 124th Meeting New Orleans 1992 October

## 4pPA6. New formulas for spherical wave reflection from an impedance
surface.

**Y. L. Li
**

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*Dept. of Elec. and Comput. Eng., Univ. of Illinois at Urbana--Champaign,
Rm. 60G Everitt Lab., 1406 W. Green St., Urbana, IL 61801
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**Michael J. White
**

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*US Army Construction Eng. Res. Lab.
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**M. H. Hwang
**

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*Univ. of Illinois at Urbana--Champaign, Urbana, IL 61801
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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.