Group velocity - Aetherwisp

The group velocity of a wave is one of two definitions of its velocity, the other being phase velocity. It is the velocity at which the envelope of the wave propagates in space. It is most easily seen in the motion of a wave packet, where the shape of the envelope is quite obvious.

The concept of group velocity only makes sense for waves composed of multiple frequencies. It is defined as

v_{g}=\frac{ \partial \omega(k) }{ \partial k }

where $\omega(k)$ is the dispersion relation between angular frequency $\omega$ and wavenumber $k$ . Since in monochromatic waves the dispersion relation is $\omega=v_{p}k$ , the group velocity is just the phase velocity:

v_{g}=\frac{ \partial (v_{p}k) }{ \partial k } =v_{p}

Wave_packet_propagation.gif|400

A wave packet showing different phase and group velocity. In this case, the phase velocity is higher. By Becarlson - Own work, CC BY-SA 4.0, from Wikipedia.