Propagation speed or wave speed are collective terms in wave theory for the speeds with which waves propagate.
For a monochromatic wave , the speed of propagation is identical to the phase speed , i.e. the speed at which a wave crest moves. In dispersive media (e.g. light in matter) this phase velocity depends on the frequency of the wave.
If you consider a spreading disturbance, i.e. a wave packet , this is composed of many monochromatic waves with different frequencies . The speed at which such a wave packet moves as a whole, i.e. the speed of the envelope , is the group speed .
For lossy propagation media or media with a non-linear dispersion relation , the shape of the wave packet can change. Therefore the group speed must be distinguished from the front speed with which a wave front propagates.
The signal speed at which information or energy is transmitted is at most as great as the front speed, while the phase and group speed of a wave can be faster, in particular faster than the speed of light in a vacuum .