Dependencies of Acoustic Properties on the Frequency and the Porosity for Biot¡?s Slow Wave in Water-saturated Copper Foams

Abstract

The present study investigated the dependencies of acoustic properties, such as the phase velocity and the attenuation coefficient, on the frequency and the porosity for Biot’s slow wave in 13 watersaturated copper foams used as trabecular-bone-mimicking phantoms. The acoustic properties were measured over a frequency range from 0.8 to 1.2 MHz by using a matched pair of broadband, unfocused transducers with a diameter of 12.7 mm and a center frequency of 1.0 MHz. The Biot model for elastic wave propagation in fluid-saturated porous media was employed to predict the experimental measurements in the water-saturated copper foams. A strong slow wave and a very weak fast wave were consistently observed in the transmitted signals for all the phantoms. The experimental phase velocity showed good agreement with that of the Biot model, increasing with the frequency and the porosity. The experimental and the theoretical attenuation coefficients were found to increase linearly or quasi-linearly with increasing frequency. In contrast, the porosity dependency of the experimental attenuation coefficient showed a behavior opposite to that of the Biot model. These results suggest that the Biot model can be usefully employed as a practical tool for predicting the phase velocity in trabecular bone, but is not suitable for predicting the attenuation coefficient.