Propagation of waves along an impedance boundary

A theoretical analysis of the scalar wave field due to a point source above a plane impedance boundary is presented. A surface wave is found to be an essential component of the total wave field. It is shown that, as a result of ducting of energy by the surface wave, the amplitude of the total wave near the boundary can be greater than it would be if the boundary were perfectly reflecting. Asymptotic results, valid near the boundary, are obtained both for the case of finite impedance (the soft‐boundary case) and for the limiting case in which the impedance becomes infinite (the hard‐boundary case). In the latter, the wave amplitude in the farfield decreases essentially as r−1, where r is the horizontal propagation distance; whereas in the former (if the surface‐wave term is neglected) it decreases as r−2. The results obtained here are compared with results of experimental studies of sound propagation along boundaries, and it is suggested that some apparently anomalous experimental findings might be explain...