The velocity and attenuation of a wave transmitted through a two-phase material are functions of the material's composition. In physical model experiments, I used suspensions of grains in a silicone rubber matrix to reduce or avoid uncertainties about framework elastic constants, porosity, and permeability that result from using fluid-saturated grain frameworks. I varied the composition to produce materials that are useful in physical seismic modeling.In the tested suspensions, ultrasonic P-wave velocity, velocity dispersion, and attenuation all increase with grain concentration and frequency. I compared seven published mathematical models for wave propagation in two-phase media. One given by Mehta most closely agrees with the P-wave velocities I observed. The agreement is sufficiently close to merit use of Mehta's model in the design of physical model materials.The observed P-wave attenuation generally increases approximately linearly with frequency. This approximate linearity leads to reliable constant-Q estimates, ranging from 187 to 16 for grain concentrations from 0 to 0.49. I conclude that relative motion between the grains and the rubber matrix contributes most of the observed attenuation at lower concentrations, whereas scattering losses become much more important at higher concentrations and frequencies.

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