Spherical wave scattering by an elastic solid cylinder—A numerical comparison of an approximate theory with the exact theory

Abstract

Numerical calculations based on an approximate theory for the problem of the scattering of a spherical wave by an elastic solid cylinder were presented in an earlier article [J. C. Piquette, J. Acoust. Soc. Am. 79, 1248–1259 (1986)]. Shortly after the appearance of this article, an exact theoretical formulation was discovered [H. P. W. Gottlieb, ‘‘On the general solution of the vector Helmholtz equation in cylindrical polar coordinates’’ J. Acoust. Soc. Am. 81, 1628–1629 (1987)]. In this letter, numerical calculations based on the exact theory are presented, and these are compared with both the approximate theory and with plane-wave theory. The calculations each involve a metallic scatterer immersed in a water medium. The approximate theory is found to give good qualitative predictions of the scattered wave in the vicinity of the scatter’s surface. The approximate theory is less reliable for increasing radial observation distances.