Significance of Group velocity Equation

The phase velocity, $v_{ph} = omega/k$, relates the period and the wave length, whereas the group velocity, $v_{g} = partialomega/partial k$, can be shown to describe (approximately) the speed of propagation of a wave packet, and therefore the speed with which information propagates (since communicating information can be understood as modulation of the wave.)

The dependence of the frequency on the wave number is often referred to as dispersion. In some media, such as vacuum, the group and the phase velocities are equal, and such media are called dispersion-less. However, this is by no means a general case - neither for the electromagnetic waves, nor for other types of waves.

The interpretation of the group velocity as the velocity characterizing propagation of information is especially relevant in relativistic domain, since the phase velocity can, in principle, exceed the speed of light, while the group velocity cannot.