Phase velocity

The phase velocity of a wave is the rate at which the phase of the wave propagates in space. This is the velocity at which the phase of any one frequency component of the wave will propagate. You could pick one particular phase of the wave (for example the crest) and it would appear to travel at the phase velocity. The phase velocity is given in terms of the wave's frequency ω and wave vector k by

Note that the phase velocity is not necessarily the same as the group velocity of the wave, which is the rate that changes in amplitude (known as the envelope of the wave) will propagate.

The phase velocity of electromagnetic radiation may under certain circumstances exceed the speed of light in a vacuum, but this does not indicate any superluminal information or energy transfer.

For light, group velocity and phase velocity are related by the formula

v_gv_p = c²

where c is the speed of light in a vacuum.

See dispersion for a full discussion of wave velocities.