The velocity at which an observable disturbance, and hence its energy, propagates. For dispersive waves (phase speed is a function of wavenumber), the speed of the wave group is generally different from the average phase speed of the individual wave components.
1. The velocity of the envelope of a group of waves of nearly equal frequencies. From the dispersion relation (Ï‰) the group velocity is defined as dk, as distinguished from the phase velocity (or phase speed. The origin of this term is made clearer by considering the superposition of two equal-amplitude plane harmonic waves with wavenumbers and frequencies Ï‰ Â± Î”Ï‰: Because , this composite wave may be looked upon as a high-frequency wave, with phase velocity Ï‰/, modulated by a wave of much lower frequency Î”Ï‰. The envelope of the high- frequency wave is a low-frequency wave propagating with the group velocity Î”Ï‰/Î”. Note the similarity with beating. Indeed, a group of waves may be looked upon as a moving beat. 2. The velocity at which a group of waves, and the wave energy, travels. In deep water, on the basis of linear water wave theory, it can be shown to be equal to one half the phase velocity.
1) The velocity of propagation of an envelope produced when an electromagnetic wave is modulated by, or mixed with, other waves of different frequencies. 2) For a particular mode, the reciprocal of the rate of change of the phase constant with respect to angular frequency. 3) The velocity of the modulated optical power. Numbers