Propagation of an ultrasonic impulse in porous media having a rigid frame

Abstract

The sound propagation in porous materials having a rigid frame filled by air, is well described by the equivalent fluid model where the interactions between fluid and structure are taken into account in the dynamic tortuosity α(ω) and in the dynamic compressibility β(ω) defined by the basic equations ρα(ω)(∂〈v〉/∂t)=−∇〈p〉, (β(ω)/Ka)(∂〈p〉/∂t)=−∇〈v〉. In the domain of the low-frequency approximation, the behavior of these response factors leads to a wave equation with a dissipative term due to the viscous effects. For high frequencies, a porous material becomes a dispersive medium in which the phase and group velocities are functions of frequency; in such a material a transient pulse changes its shape by spreading. A theoretical model of the sound propagation in a dispersive porous material is presented. This problem is posed in the time domain for an ultrasonic pulse in a slab of porous material. A method is proposed for computing the sound field in the medium. This allows one to deduce the transmission and reflection coefficients which are dependent only on the physical parameters of the medium (but not of the incident wave), which is important for inverse problems. The spreading of the transient pulse is calculated for various porous media and compared to experimental data.