Diffraction of sound pulses by a circular cylinder

Abstract

The diffraction of sound pulses by a circular cylinder in a fluid medium is analyzed by applying the Poisson's summation formula and Laplace transform. The inverse Laplace transform is computed analytically by using a modified Cagniard method. This newly developed method avoids the tedious calculation of residues of complex-ordered Bessel functions. Because asymptotic approximations of the modified Bessel functions have been used, the solutions so obtained are good for the early-time transient waves or for pulses with short duration, for which the normal-mode solution is poorly convergent. Analytical solutions for the incident, reflected and diffracted pulses in the illuminated and shadow zones are obtained by a unified approach. Each pulse is represented by a ray integral with a unique arrival time which conforms to Fermat's principle. The numerical results obtained for an incident square pulse emitted by a line source resemble the actual experimental observations reported by others [G. R. Barnard and C. M. McKinney, J. Acoust. Soc. Am. 33, 226 (1961)] for the backscattering of a hard cylinder in water. [Supported by NSF through a grant to the Materials Science Center at Cornell University.]