Andrey V. Osipov
Radiophys. Dept., Inst. of Phys., St. Petersburg State Univ., Ulianovskaya 1-1, 198904 St. Petersburg, Russia
Diffraction of waves by a wedge is one of the several canonical problems of modern acoustics whose mathematical solutions provide a theoretical basis in analyzing sound radiation and scattering phenomena. Starting from Sommerfeld's classical works, considerable attention has been attracted to this class of diffraction problems, especially to the particular cases of a perfectly reflecting wedge and half-plane [W. J. Hadden and A. D. Pierce, J. Acoust. Soc. Am. 69, 1266 (1981); R. P. Kendig and S. I. Hayek, J. Acoust. Soc. Am. 70, 1156 (1981)]. 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 that remains to be correct at shadow boundaries. 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 depending on the values of face impedances are described.
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