3. Conservation equations

The equations for the propagation of an acoustic wave in a compressible fluid or an elastic solid can be deduced from the equations for the conservation of matter, momentum and energy. To write these equations, we adopt the Eulerian description of motion: all physical quantities are represented by functions of time t and position x in the reference frame, assumed to be Galilean, and we consider any fixed volumeV inside the medium. In the case of a fluid, the boundary surface S is traversed by particles as they move.