Approximate models for sound propagation above multi-impedance plane boundaries

Abstract

The propagation of sound over an infinite plane with various distributions of surface impedance is considered. Three methods are used to calculate the sound field. The first is a numerical solution based on a boundary integral equation formulation of the problem. Although involving some approximation this approach provides accurate results for a wide range of propagation conditions in a still homogeneous atmosphere but suffers from the need for large computing resources. The other two methods are approximate but have the advantage that they are easy and efficient to calculate. The first of these involves empirical modification of the equation for diffraction of monopole radiation by a rigid half-plane, proposed by de Jong. In the other the sound field at the receiver is assumed to be governed by the surface conditions in a region around the specular reflection point. This region is defined by a Fresnel-zone condition. Results using the three approaches are compared for a large range of source and receiver positions and for the following boundary conditions: (i) A straight discontinuity between two surface impedances perpendicular to the source–receiver path, (ii) a straight discontinuity between two surface impedances parallel to the source–receiver path, and (iii) a strip of different impedance perpendicular to the source–receiver path. Comparison is also made with the results of model experiments for surface conditions when the discontinuity is parallel to the direction from source to receiver. The computational time for the boundary integral equation calculations is dependent on the frequency of the source and the site geometry, but in all cases was several orders of magnitude greater than the computation times for the other two methods. Calculation times for these two methods was very short since they essentially involved only the enumeration of a formula. The de Jong approach proved flexible in application to all the boundary conditions considered and agreed well with the boundary integral equation and the experimental results except in one case of propagation over a strip when the grazing angle was very small. The Fresnel-zone method adequately described the general trends in the results of the other two methods. Possible extensions of this method to more complex distributions of ground cover and allowance for atmospheric effects are discussed.