On sound diffraction by an impedance wedge

Abstract

Diffraction of waves by a wedge is a problem of modern acoustics whose mathematical solutions provide a theoretical basis in analyzing sound radiation and scattering phenomena. Considerable attention has previously been attracted to this class of diffraction problems, especially to the particular cases of a perfectly reflecting wedge and half-plane. The model of an impedance wedge [G. D. Malyuzhinets, 1958 Dokl. Akad. Nauk SSSR 121, 436 (1958) in Russian] is a more general and realistic one that gives new opportunities for treating acoustic diffraction by irregular surfaces [A. D. Pierce and W. J. Hadden, J. Acoust. Soc. Am. 63, 17 (1978); A. V. Osipov, Sov. Phys. Acoust. 36, 287 (1990)]. This paper investigates the wave field excited by a line source in the presence of a wedge with arbitrary values of face impedances. Based on the Malyuzhinets’ solution, various exact representations for the Green’s function are deduced to generate a system of convenient formulas for any relative positions of the source and point of observation. A new representation of the Malyuzhinets’ solution in the form of double series [A. V. Osipov, Sov. Phys. Acoust. 37, 381 (1991)] is exploited to describe the wave field of the line source placed in the vicinity of edge. In the opposite case of large distances from the edge, a uniform asymptotic expansion is presented. Applications of the obtained results to problems of sound attenuation by wedge-like barriers and sound radiation from a line source located at the edge of a corrugated surface are described.