Plane wave diffraction by a wedge with finite impedance

Abstract

A theory is presented for the diffraction of acoustic waves by barriers with finite acoustical impedance, the shape of the barriers being such that, insofar as diffraction into the shadow zone is concerned, they may be idealized as semi-infinite wedges. The analytical development is based on the known exact solution for plane wave diffraction by a finite impedance wedge, versions of which have been previously given in the literature by Williams [Proc. R. Soc. London Ser. A: 252, 376–393 (1959)], by Senior [Commun. Pure Appl. Math. 12, 337–372 (1959); Proc. R. Soc. London Ser. A: 213, 436–458 (1952)], and by Maliuzhinets [Sov. Phys. Acoust. 1, 152–174; 240–248 (1955)]. This solution is described in detail and the asymptotic limit is derived in a form which demonstrates the satisfaction of the reciprocity principle. Practical implementation is discussed, both through numerical examples and through the presentation of graphs of quantities which will be helpful in barrier design.