Conventional acoustical methods for measuring the permeability or flow resistivity of a porous material require a priori estimation of the porosity. In this work, an acoustical method is presented in which a simplified expression (independent of both the frequency and porosity) for the transmitted waves at the Darcy's regime (low frequency range) is derived, and used for the inverse determination of both the viscous static permeability (or flow resistivity) and the thickness of air-saturated porous materials. The inverse problem is solved based on the least-square numerical method using experimental transmitted waves in time domain. Tests are performed using industrial plastic foams. Experimental and numerical validation results of this method are presented, which show the advantage of measuring the viscous permeability and thickness of a porous slab, without the required prior knowledge of the porosity, but by simply using the transmitted waves.

An acoustic reflectivity method is proposed for measuring the permeability or flow resistivity of air-saturated porous materials. In this method, a simplified expression of the reflection coefficient is derived in the Darcy's regime (low frequency range), which does not depend on frequency and porosity. Numerical simulations show that the reflection coefficient of a porous material can be approximated by its simplified expression obtained from its Taylor development to the first order. This approximation is good especially for resistive materials (of low permeability) and for the lower frequencies. The permeability is reconstructed by solving the inverse problem using waves reflected by plastic foam samples, at different frequency bandwidths in the Darcy regime. The proposed method has the advantage of being simple compared to the conventional methods that use experimental reflected data, and is complementary to the transmissivity method, which is more adapted to low resistive materials (high permeability).

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