Sound wave propagation from a point source over a homogeneous surface and over a surface with an impedance discontinuity

Abstract

The sound field from a point source above an infinite plane with an impedance discontinuity is studied by considering the Helmholtz equation. With boundary conditions the Helmholtz equation is transformed into a singular integral equation and an exact solution formula is given. The formula is evaluated for the case when the source and the receiver are close to the boundary, many wavelengths from the discontinuity. The evaluation gives, among other things, information on the dependence of the surface wave structure on the impedances and—in the case of no surface waves—information on the farfield solution. If one of the impedances gives a surface wave in the case of a homogeneous boundary, then a surface wave appears also in the nonhomogeneous case and is modified depending on the other impedance. In the case of no surface waves, the rapid decay of the sound field in the homogeneous case does not appear in the nonhomogeneous case since the discontinuity acts as a weak source of slowly decaying waves. A number of experiments are suggested by the results. A new treatment of the special case of a homogeneous boundary is also given, with a new asymptotical expansion of the solution.