Characteristic velocity and dispersion relation of linear waves in extended thermodynamics of a van der Waals gas

We study the characteristic velocities of the extended thermodynamics of molecular rotational- and vibrational- relaxation processes for a van der Waals gas. The lower and upper bounds of the characteristic velocity are, respectively, estimated by the one of rarefied gases and the one evaluated on the spinodal curve. We also study the dispersion relation of linear waves, in particular, the phase velocity, attenuation factor and attenuation per wavelength in a low frequency region.