Given a linear relationship between ``generalized'' displacements and ``generalized'' forces, we can derive wave equations for elastic, electromagnetic and thermal quantities. The derivation of the individual wave equations follows a common procedure: first, finding a conservation law for the generalized stress-like and strain-like quantities, and, second, finding a constitutive relationship (linear law) between those quantities. Here the constitutive law can also include alien stress- or strain-like quantities. Using the conservation and constitutive relationships, I can find a wave equation for each type of quantity. It is in fact a coupled system of equations which have to be solved simultaneously.
The advantages of using elastic displacements as observable quantities are the speed of computation and the formal similarity to the conventional Christoffel equation. However, if, instead of displacements, elastic strains are used to describe wave propagation, the wave equation resembles more the generalized linear relationship between stresses and strains. In a few instances boundary conditions may be easier to specify in terms of strain variables. However this method, given in the appendix, is more costly.