The present paper analyses models describing wave absorbing materials from a thermodynamic point of view. This study deals with harmonic plane wave propagation through a viscoelastic homogeneous medium at the macroscopic scale. The dynamic behaviour of the studied medium is modelled using two distinct complex functions related to the bulk and to the density, respectively. It is shown that the complex density function results from viscous body forces. This paper aims to discuss the thermodynamic constraints on these acoustic models for a general onedimensional (1D)-harmonic plane wave system. The dynamic intrinsic dissipation of the studied viscoelastic medium is defined and evaluated. Using the second law of thermodynamics, conditions are found to define consistent functions modelling the dissipative effects. The classical rigid open porous model used to describe many sound absorbing media is taken as an example for such a harmonic viscoelastic model. It demonstrates that the main dissipative phenomenon can be described using a complex density function.