Theory of acoustical edge waves

Abstract

The physical theory of diffraction is applied to acoustical diffraction problems, using the concept of elementary edge waves scattered in the vicinity of an infinitesimal edge element. Far from the edge element, these elementary edge waves are described by the circular function of complex arguments. Various definitions of elementary edge waves are discussed. The theory is formulated in general form, namely for the scattering surfaces with arbitrary sharp edges. Faces of edges are assumed to be acoustically soft or hard and the edges themselves are assumed to be smoothly curved (in terms of wavelength). An angle between faces varies slowly along the edge. This theory enables one to calculate the dominant term in the high-frequency asymptotic expansion for primary and multiple edge waves. Asymptotics of this kind are found for the scattered field in the ray region, near a smooth caustic, on the shadow boundary, and along a focal line. The connection between the physical theory of diffraction and other asymptotic methods is established.