Cross sections are computed for the scattering of a plane transverse wave from a spherical cavity embedded in an infinite, isotropic, homogeneous, elastic solid. Analytical expressions are derived for the matrix elements indicated by Einspruch, Witterholt, and Truell, and the resulting matrix equations are solved numerically. The dependence of the scattering cross section upon K1a (K1 is the transverse propagation constant, a is the cavity radius) over the range 0.01–10 is computed for various host materials, and the results are compared with the case of incident longitudinal waves computed by Johnson and Truell. The sensitivity of the cross section to the elastic properties of the medium, and the behavior in the Rayleigh limit approximation are discussed. The relative contributions of the various components of both the longitudinal and transverse scattering cross sections are isolated, and their dependence upon K1a, k1a (k1 is the longitudinal propagation constant) and host material is elucidated. A peaking behavior analoguous to that occurring in the longitudinal case is observed in the longitudinal component of the scattered transverse wave.
Measurements of ultrasonic attenuation due to the scattering of longitudinal elastic waves from a distribution of cavities in a solid medium are found to be consistent with theoretical predictions. Under certain conditions such measurements can be utilized to nondestructively characterize the size and number density of such a collection of scatterers.
The ultrasonic pulse-echo technique has been used to study the absorbtion due to scattering of longitudinal waves from cavities in a solid, in the range of ka from 0.03 to 4.5 (k is the longitudinal wave vector, a the cavity radius). Experimental results obtained from specimens of sintered tungsten bars and pore-bearing tungsten filaments are consistent with the theory of Ying and Truell [J. Appl. Phys. 27, 1086 (1956)] for the scattering of a longitudinal wave from a single spherical cavity embedded in an elastic medium. Metallographic analysis revealed that both types of specimens contain narrow distributions of scatterer radii, centered at 20 μ in the filaments and 2 μ in the sintered bars. These results, along with the frequency dependence of the attenuation measured from 5 to 350 MHz, were used in conjunction with the theory to obtain estimates of the number density of scattering centers. Analytical techniques for extracting the scattering contribution from the total attenuation are discussed.
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