Backscattering from an elastic sphere: Sommerfeld–Watson transformation and experimental confirmation

Abstract

The Sommerfeld–Watson transformation (SWT) of the partial wave series for the acoustical scattering from a fluid-loaded elastic sphere is examined. This research specifically focuses on the specular reflection and Rayleigh wave contribution to scattering at small backscattering angles. In a previous paper the angular dependence of the Rayleigh contribution to near backward scattering was measured and modeled [Williams and Marston, J. Acoust. Soc. Am. 78, 722–728 (1985)]. The SWT confirms the physical picture used and, for the first time, predicts the absolute Rayleigh contribution associated with one or more circumnavigations of the sphere. To test the SWT, tungsten carbide spheres in water were ensonified by tone bursts having central frequencies in the range 24<ka<80. Measurements were made of the first and second Rayleigh contributions to the backscattered pulse train. Plots of these measured distinct Rayleigh amplitudes as a function of ka confirm the results of the SWT and illustrate the significance of radiation damping and axial focusing.