Propagation of sound and the assignment of shape factors in model porous materials having simple pore geometries

Abstract

The acoustical properties of a class of simple porous materials have been studied experimentally and theoretically. Rigid-frame materials containing air-filled pores of uniform cross section were investigated. Two model porous materials were constructed, one with pores of rectangular cross section (0.0146×0.0172 cm) and one with pores of triangular cross section (0.037-cm sides). The characteristic impedance and propagation constant were measured for frequencies between 50 and 4500 Hz and good agreement with exact theoretical predictions was obtained. The exact theoretical expressions for specific pore shapes (e.g., slitlike, square, and triangular) can be used to investigate the assignment of shape factors by various general but approximate theoretical models. It is demonstrated that the model introduced by Attenborough requires a shape factor that is frequency dependent. A theoretical model, appropriate for materials containing pores of uniform cross section, that correctly treats the low- and high-frequency behavior, is presented. Given subsidiary measurements of flow resistivity, porosity, and tortuosity, a single shape factor leads to very good agreement with the exact solutions for all frequencies.