1

The medium is spatially homogeneous and isotropic at equilibrium.

2

Elastic properties of the medium can be treated in terms of linear elasticity.

3

The medium is close to the equilibrium state sufficiently in order to neglect deviatoric component (2.4) of the total stress (2.2) (see also (2.5)).

4

The medium is assumed to be isothermal. As is well known (e.g., [16] , p. 617), acoustical vibrations are almost always so rapid that there is no time for conduction to remove the heat developed and equalize the temperatures. The contractions and expansions take place adiabatically, i.e. without loss of heat. In spite of that, the above assumption on the isothermalness is used. The reason is avoiding the need in description of the spatiotemporal evolution of the temperature in the medium and, thereby, keeping the complexity of the model at a reasonable level. This in particular means that the aforementioned heat is neglected.

5

There are no chemical reactions in the medium.

6

There are no body forces in the medium.

7

If the medium is not a linear solid, then inequality (A.1.13) holds. According to Proposition A.3.1, this inequality can be replaced with (A.3.7).

8

The medium is close to the equilibrium state sufficiently in order to replace in (A.3.2) with its equilibrium value.

9

The medium is close to the equilibrium state sufficiently in order to neglect velocity in expression (A.3) thereby reducing it to (B.5).