Short-wavelength acoustic diffraction by prolate spheroids

The scattering of a plane acoustic wave by a rigid prolate spheroid of large fineness ratio is investigated analytically. The solution for the diffracted field is presented in terms of the classic modal series of spheroidal harmonics. The series are numerically evaluated for wavelengths much smaller than the length of the spheroid, but comparable to the minor radius. For this range of wavenumbers, use was made of available asymptotic formulas of the spheroidal wave functions, where the convergence of the double infinite series is discussed in terms of the value of the product of wavenumber and various characteristic lengths of the spheroid. The directivity functions are presented for several values of plane-wave incidence, reduced frequency, and fineness ratio. The total scattering cross section is evaluated and compared to the scattering cross section of rigid spheres. An estimate is given to the size sphere required to scatter approximately the same power as the spheroid of given size and orientation with respect to the incoming plane wave. Subject Classification: 20.15, 20.30.