A theory is outlined for the propagation constant in media containing numerous small spherical particles. Using expressions derived by Lamb for the zero and first-order scattering coefficients of a particle free to move in a sound field, an expression for the complex propagation constant is derived whose real part yields a velocity which reduces to the homogeneous case for extremely small particles, and whose imaginary part yields an absorption coefficient identical with that derivable from the viscous-drag theory outlined in a previous paper. Using both an interferometer and a pulse-reflection method, measurements of sound velocity and absorption at megacycle frequencies have been made on mercury-in-water and bromo-form-in-water emulsions of non-uniform particle size, up to a volume concentration of about 50 percent of emulsified liquid. These materials, though showing considerable deviation from a homogeneous behavior, are found to have a velocity and absorption in good agreement with the theory up to concentration of about 25 percent by volume.
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Urick et al. (1949) studied this question.