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The group velocity is positive (i.e., the envelope of the wave moves rightward), while the phase velocity is negative (i.e., the peaks and troughs move leftward). The group velocity of a wave is the velocity with which the overall envelope shape of the wave's amplitudes —known as the modulation or envelope of the wave—propagates through space.
Propagation of a wave packet demonstrating a phase velocity greater than the group velocity. This shows a wave with the group velocity and phase velocity going in different directions. The group velocity is positive, while the phase velocity is negative. [1] The phase velocity of a wave is the rate at which the wave propagates in any medium.
In dispersive media the phase velocity is not necessarily the same as the group velocity. The phase velocity varies with frequency. The phase velocity is the rate at which the phase of the wave propagates in space. The group velocity is the rate at which the wave envelope, i.e. the changes in amplitude, propagates. The wave envelope is the ...
Phase velocity is the rate at which the phase of the wave propagates in space: any given phase of the wave (for example, the crest) will appear to travel at the phase velocity. The phase velocity is given in terms of the wavelength λ (lambda) and period T as =. A wave with the group and phase velocities going in different directions. Group ...
The group velocity is depicted by the red lines (marked B) in the two figures above. In shallow water, the group velocity is equal to the shallow-water phase velocity. This is because shallow water waves are not dispersive. In deep water, the group velocity is equal to half the phase velocity: {{math|c g = 1 / 2 c p. [7]
Inherent in these equations is a relationship between the angular frequency ω and the wave number k. Numerical methods are used to find the phase velocity c p = fλ = ω/k, and the group velocity c g = dω/dk, as functions of d/λ or fd. c l and c t are the longitudinal wave and shear wave velocities respectively.
Phase velocity, the velocity at which a wave phase propagates; Pulse wave velocity, the velocity at which a pulse travels through a medium, usually applied to arteries as a measure of arterial stiffness; Group velocity, the propagation velocity for the envelope of wave groups and often of wave energy, different from the phase velocity for ...
It is possible to calculate the group velocity from the refractive-index curve n(ω) or more directly from the wavenumber k = ωn/c, where ω is the radian frequency ω = 2πf. Whereas one expression for the phase velocity is v p = ω/k, the group velocity can be expressed using the derivative: v g = dω/dk. Or in terms of the phase velocity v p,