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Group velocity refers to the velocity at which the overall envelope of a wave packet, such as a pulse of light or a matter wave, propagates. This is in contrast to phase velocity, which describes the speed at which a single phase point of the wave, like a crest, moves. In many cases, particularly in non-dispersive media, the group velocity and phase velocity are equal. However, in dispersive media, where the phase velocity depends on the frequency or wavelength of the wave, the group velocity can be different from the phase velocity.

The group velocity is a crucial concept in understanding wave propagation, especially in fields like optics and quantum mechanics. For example, in optical fibers, the dispersion of light pulses leads to different frequencies traveling at different speeds, which is described by the group velocity. This phenomenon affects the transmission of data. In quantum mechanics, the group velocity of a matter wave packet corresponds to the classical velocity of the particle. If the group velocity is greater than the speed of light in a vacuum, it does not violate relativity, as it is the envelope's speed, not the speed of information transfer. The mathematical definition of group velocity often involves the derivative of the angular frequency with respect to the wave number.