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 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.

The Sound Velocity in Ideal Liquid Mixtures from Thermal Volume Fluctuations

“…This expression is known from the literature as the Urick equation, [30,31] and the formalism is frequently applied for the investigation of sound propagation in mixtures (see e.g. ref.…”

Sonocrystallization: The End of Empiricism?

“…They differ from the physical mechanisms of ultrasonic propagation that they describe. The model by Urick [32,33,34] is phenomenological, the model of Harker et al is hydrodynamical [35,36], and the model of Allegra and Hawley [37] is based on scattering.…”

Viscous attenuation of acoustic waves in suspensions

“…One of the earliest applications of the scattering formulation for spherical particles was by Urick and Ament (1949), who used the zero and first-order scattering terms to estimate phase velocity and attenuation. The existence of shear waves in the scattering particles was incorporated into scattering theory by Faran, Jr. (1951).…”