On the propagation of linear longitudinal acoustic waves in isotropic media with shear and volume viscosity and a tensorial internal variable: II. Some cases of special interest (Poynting-Thompson, Jeffreys, Maxwell, Kelvin-Voigt, Hooke and Newton media)

Abstract

In a previous paper the propagation of linear longitudinal acoustic waves in isotropic media with shear and volume viscosity and a tensorial internal variable was considered and the expressions for the velocity and attenuation of the waves were obtained. In the present paper we investigate the propagation of linear longitudinal acoustic waves in Poynting-Thomson, Jeffreys, Maxwell, Kelvin-Voigt, Hooke and Newton media. We show that the dispersion relations for these waves may be considered as degeneracies of the dispersion relation which we derived in the general case of a viscoanelastic medium with memory. In particular we investigate the explicit dependence of the dispersion relations on the thermodynamic parameters and the phenomenological coefficients and the limiting cases of waves with high and low frequencies are discussed.