A note on wave propagation in internally constrained hyperelastic materials

The purpose of this note is to recall and give simple proofs of general results relating to the speeds of propagation and polarization of waves propagating in internally constrained materials. Some of the results have been given previously but appear not to be as well known as they ought to be. Typical of the results is that for an incompressible hyperelastic body the squared wave speeds are real and the corresponding polarizations are orthogonal.