Acoustic scattering by a spherical obstacle: modification to the analytical long-wavelength solution for the zero-order coefficient

Classical long wavelength approximate solutions to the scattering of acoustic waves by a spherical liquid particle suspended in a liquid (an emulsion) show small but significant differences from full solutions at very low kca (typically kca < 0.01) and above at kca > 0.1, where kc is the compressional wavenumber and a the particle radius. These differences may be significant in the context of dispersed particle size estimates based on compression wave attenuation measurements. This paper gives an explanation of how these differences arise from approximations based on the significance of terms in the modulus of the complex zero-order partial wave coefficient, A0. It is proposed that a more accurate approximation results from considering the terms in the real and imaginary parts of the coefficient, separately.