The Propagation of an Acoustic Wave along a Boundary

The sound field of a point source near the boundary of two media cannot be obtained by an acoustic-ray approach. In fact, such an approach which utilizes the reflection coefficient for plane waves leads to completely contradictory results at grazing incidence. A more rigorous solution is obtained, the procedure followed being exactly similar to that initiated by Sommerfeld to derive the electromagnetic field of a vertical dipole situated near a conducting plane. The results of such an analysis as applied to an acoustic point source are presented. As pointed out by Van Der Pol, the resultant solution may be regarded as that due to the point source and a diffuse image. The discussion of the solution is restricted to cases in which the sound source is at the boundary although it is given for all source heights. The solution shows that when the boundary medium has a high real specific acoustic impedance, non-zero fields are obtained at all points along the boundary. For bounding media adequately described by simple porosity theory, the acoustic pressure at the boundary is inversely proportional to the square of the distance and the square of the frequency, at reasonably large distances and low frequencies. Also there appears to be decreased phase velocities along the boundary. Some calculations of the sound pressure as a function of height above Quietone show, among other things, the presence of a minimum occurring some distance above the boundary. At large distances from the source there are very large decreases in amplitude as the receiver height is increased in the region above this minimum.