Diffraction Effects in a Random Sound Field

Abstract

When making measurements in random sound fields, for example in a reverberant enclosure, it is desirable to know what diffraction effects occur at a reflecting object such as a transducer, suspended in the enclosure. In the case of a sound field consisting of a traveling plane-wave train, the diffraction effects for spheres and cylinders have been well studied, and various analytical results are available. Some of these results are here extended to the case of a randomly incident sound field. The potential and kinetic energy distributions in the vicinity of a rigid reflecting sphere under random incidence are derived as functions of the diameter of the sphere in wavelengths. Corresponding results for a pressure-release boundary condition at the surface of the sphere, and for an infinite circular cylinder in a two-dimensional random field, are also given. The general effect of boundary configuration on diffraction pattern is discussed, and the random field pressure at the vertex of a wedge-shaped reflector of arbitrary angle is considered as an example. The diffraction effects are basically reciprocal, and the correspondence of the results with those for the reciprocal cases is discussed. Some practical applications of the results are considered.