David W. Craig
Carl K. Frederickson
James M. Sabatier
Natl. Ctr. for Phys. Acoust., Univ. of Mississippi, University, MS 38677
Probe microphones have been developed to determine tortuosity and effective flow resistivity for air-filled porous materials, such as agricultural soils. They are used to measure complex wave number as a function of frequency. These data are then inverted using a single-pore-size capillary tube model for propagation in the material. However, the frequency dependence of the measured wave number in sand differs from the predictions of such single-scale models. It is shown that distributions of pore sizes can produce a similar dependence. By summing over pore sizes, wave number as a function of frequency is calculated for lognormal, fractal (power-law), and empirical distributions derived from porosimetry data. Results are also compared with Wilson's relaxation-matched fractal model [D. K. Wilson, J. Acoust. Soc. Am. 94, 1136--1135 (1993)]. [Work supported by USDA.]