The concept of energy velocity for linear dispersive waves is usually given for a normal mode solution of the system as the ratio between the mean energy flux and the mean energy density. In the absence of dissipation this velocity is known to coincide with the corresponding group velocity. When dispersion is accompanied by dissipation, this interpretation is not correct since the group velocity loses its original meaning and can assume nonphysical values. In this note the relation between energy velocity and group velocity is derived for dissipative, uniaxial waves, governed by a linear hyperbolic system. An example is provided where the energy velocity is compared with the phase and group velocities.
- Classical mechanics of continuous media
- general mathematical aspects