Low-frequency expansions for acoustic wave scattering using Waterman’s T-matrix method

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Abstract
Analytical expressions are derived for the T-matrix elements of cylindrical and spheroidal inclusions and cavities as an expansion in powers of the nondimensional wavenumber ka. For plane monochromatic acoustic wave incidence, analytical expressions are presented for the farfield scattered amplitude. These expressions are compared with existing, exact results using Mathieu functions and spheroidal functions. The agreement is shown to be exact to any given order in ka, giving a strong indication that at least in the farfield the T matrix leads to the proper asymptotic expansion in ka.

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