Rayleigh‐mode backscattering from an elastic sphere: Sommerfeld‐Watson transformation and experimental confirmation

The acoustical scattering form function of fluid‐loaded bodies such as cylinders and spheres may be written as a partial wave series. The Sommerfeld‐Watson transformation (SWT) has been used previously to rewrite the form function of elastic cylinders with ka⩾1. The SWT allows one to understand the form function in terms of reflected, transmitted, and surface waves. In the present discussion we carry out the SWT on a fluid‐loaded elastic sphere. We concentrate on the specular reflection and Rayleigh wave contribution to scattering at small backscattering angles. We previously measured and modeled the angular dependence of the Rayleigh contribution to near backward scattering [K. L. Williams and P. L. Marston, J. Acoust. Soc. Am. Suppl. 1 76, S8 (1984)]. 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 30 < 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. [Work supported by ONR.]