Enhancement of the backscattering of high-frequency tone bursts by thin spherical shells associated with a backwards wave: Observations and ray approximation

Abstract

A prominent feature predicted for the backscattering of tone bursts by thin spherical shells is an enhancement of a guided wave contribution near the first longitudinal resonance. This has been explained with a backward ray model of a leaky Lamb wave where energy is leaked off without having circumnavigated the far side of the shell [P. L. Marston et al., J. Acoust. Soc. Am. 90, 2341 (1991); D. H. Hughes, Ph.D. thesis, Washington State University (1992)]. The relevant s2b Lamb wave has opposing group and phase velocities giving rise to prompt radiation following the direct specular echo. The present research gives a comparison between a ray theory approximation and experiments in which tone bursts having carrier frequencies in the range 585<ka<630 were incident on an empty stainless-steel spherical shell of radius a=12.7 cm in water. The sphere’s thickness to radius ratio is approximately 0.02. Measurements of the superposition of the specular reflection and s2b Lamb wave contribution agree with the predicted amplitudes and are nearly a factor of 5.5 larger than the reflection from a rigid sphere of the same size. The calculated properties of the s2b wave are compared with calculations for a shell in vacuum.