Frequency dependence of ultrasonic velocity and attenuation in two-phase composite systems with spherical scatterers

Abstract

The frequency dependence of the scattering contribution of ultrasonic attenuation and sound velocity of longitudinal waves was measured in a frequency range from 2 to 50 MHz. For model systems we used gelatine samples with 20 wt % glass beads of 315–400 μm and 180–250 μm diameter and with 10 wt % glass beads of 42–174 μm diameter. The application of a recently developed Fourier transform technique allowed us to observe both ultrasonic attenuation and velocity with sufficiently high accuracy for quantitative comparison with sound scattering theory. The frequency dependence of sound attenuation shows multiple maxima, whereas in the frequency dependence of the velocity difference a sharp minimum on the order of 1% of the absolute velocity occurs. For the simulation of ultrasonic attenuation and sound velocity we combined a multiple scattering approach from Waterman and Truell [J. Math. Phys. 2, 512 (1961)] with a acoustic resonance scattering theory for a viscoelastic sphere developed by Ayres and Gaunaurd [J. Acoust. Soc. Am. 81, 301 (1986)]. Supplementary in the computations, the attenuation of the matrix and the particle size distribution were taken into account. Comparison of the simulated data to the experimental results shows good agreement.