On sound energy scattered by a rigid body near a compliant surface

A theorem is derived which generalizes the classical extinction theorem (also known as the optical theorem) to cases where a rigid scatterer of arbitrary shape is lo­cated near a large compliant surface which has quite general mechanical properties, including dissipation and wave-bearing features, and where the acoustic media on both sides of the compliant surface may have different densities and sound speeds. The theorem relates the sound energy scattered from incident planar acoustic waves to the far field pressure in the specular reflection direction and that in the transmis­sion direction, determined by the Snell’s law. From this simple relation, the scattered energy can be found almost trivially from the far field pressures in these two partic­ular directions; the energy calculation then completely avoids integration of energy flux over control surfaces.