Diffraction of sound by hard strips and truncated wedges

Abstract

Starting from rigorous diffraction solutions for single, hard, semi‐infinite wedges, it has long been possible to construct approximate solutions for more complex angular surfaces [A.D. Pierce, J. Acoust. Soc. Am. 55, 941–955 (1974)]. Demonstrated here is an exact procedure that formulates the multiple scatter between vertices of an angular body via the standard self‐consistent algorithm. This allows one to obtain the correct diffracted field of each vertex. Summing these together with the relevant incident and image fields leads to an exact solution for the full sound field. This is done here for the case of a plane harmonic incident sound field for (1) a truncated wedge and (2) a hard strip of width l. Numerical results for the latter model are shown to compare satisfactorily for all kl with experimental data [H. Medwin et al., J. Acoust. Soc. Am. 72, 1005–1013 (1982)]. This theoretical procedure yields, in the plane wave case, a formal estimate of the error incurred in the “double diffraction” approximation (i.e., the procedure that neglects all but the first two terms of the multiple scatter series). This error decreases like elkl/kl for increasing kl. It is then possible to confirm theoretically the observation of Medwin et al. who showed that, for the geometry of their strip experiment, this approximation is actually very good for kl≳ 3 and quite adequate in the region 1 < kl < 3, using the Biot‐Tolstoy rigorous impulsive point source solution for the perfect wedge [M. A. Biot and I. Tolstoy, J. Acoust. Soc. Am. 29, 381–391 (1957)] for their double‐diffraction solution. [Work supported by ONR.]