Group velocities

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group velocity

  1. The velocity of the envelope of a group of waves of nearly equal frequencies.

    From the dispersion relation k(ω) the group velocity is defined as dω/dk, as distinguished from the phase velocity (or phase speed) ω/k. The origin of this term is made clearer by considering the superposition of two equal-amplitude plane harmonic waves with wavenumbers k ± Δk and frequencies ω ± Δω:
    , this composite wave may be looked upon as a high-frequency wave, with phase velocity ω/k, modulated by a wave of much lower frequency Δω. The envelope of the high- frequency wave is a low-frequency wave propagating with the group velocity Δω/Δk. 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.