The Propagation of Sound in Composite Media

Abstract

A theory is outlined for the propagation constant in media containing numerous small spherical particles. Using expressions derived by Lamb for the zeroth- 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 bromoform-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 a concentration of about 25 percent by volume. Similar measurements on suspensions of quartz sand in water exhibit small deviations of velocity from the theory that may possibly be attributed to the non-spherical shape of the quartz particles.