On the propagation of linear longitudinal acoustic waves in isotropic media with shear and volume viscosity and a tensorial internal variable

In this paper we consider the propagation of linear longitudinal acoustic waves in isotropic media with viscosity and a tensorial internal variable. We use a thermodynamic theory for mechanical relaxation phenomena proposed by one of us in some previous papers. In particular we investigate the velocity and attenuation of the waves and we consider the limiting cases of high and low frequencies. We show that at high frequencies the tensorial internal degree of freedom does not influence the wave phenomena. If the frequencies are sufficiently low, the phase velocity depends only on the coefficients which occur in the equations of state, while the attenuation of the waves also depends on the coefficients which occur in the phenomenological equations which describe the irreversible processes of viscous flow and changes in the tensorial internal variable.