Use of Sound Pulses for a Study of Circumferential Waves

Abstract

In recent underwater experiments, multiple echoes that returned in the scattering of a single pulse have been tentatively analyzed in terms of creeping (or circumferential) waves appearing in the diffraction process. In other experiments, the presence of creeping waves has been inferred from steady-state interferences. It is suggested here that one should confirm the existence of circumferential waves by observing diffracted pulses in the near field around the scatterer, including the shadow region. A mathematical study of the creeping waves is performed, using the Sommerfeld-Watson transformation method of Franz and assuming that the initial plane sound wave possesses an arbitrary pulse shape. The expressions for the creeping pulses obtained on the surface of the scatterer include—but go beyond—previous results of Friedlander, found with a different method; we also considered geometrically reflected pulses and farfield expressions. The special example of an infinitely long, acoustically soft, circular cylinder is used, but an extension to other simple cases is possible. Some examples are discussed graphically.