On acoustical models for sound propagation in rigid frame porous materials and the influence of shape factors

Abstract

The propagation of sound in rigid-frame porous materials saturated with air is studied experimentally and theoretically. Two existing theoretical models, the Attenborough and the Biot–Allard models, are first evaluated using measured characteristic impedances and propagation constants for samples of ceramic material. The Biot–Allard model is found to give good agreement to the measured data if a single, frequency-independent shape factor is introduced. The Attenborough model, though, requires a shape factor that has a significant frequency dependence. To provide a more stringent test, we have constructed a model porous material that has large variations in pore cross-sectional area. This sample contains 373 straight cylindrical pores whose diameters alternate between 0.025 and 0.154 cm along their lengths. Both the Biot–Allard and Attenborough models are unable to describe the measured acoustical properties for this sample. A simple theoretical model is proposed that describes the propagation of sound through pores whose cross-sectional area and shape change along the course of each pore in a known fashion. Very good agreement between experimental results and the theoretical predictions for the two-diameter model is found. It is demonstrated that the dynamic density function (that describes the viscous effects) is associated more with the narrow sections of the pores and the dynamic bulk modulus (describing the thermal effects) is associated more with the wider sections of the pores. This theoretical model for arbitrary materials can then be generalized. Two different shape factors are required, in general, to describe both the viscous and thermal effects.