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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.
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. [1] 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 ...
Download as PDF; Printable version; In other projects ... The group velocity is one half the phase velocity. A wave in which the group and phase velocities differ is ...
The notion of group velocity is based on a linear approximation to the dispersion relation () near a particular value of . [6] In this approximation, the amplitude of the wave packet moves at a velocity equal to the group velocity without changing shape. This result is an approximation that fails to capture certain interesting aspects of the ...
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]
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 and group velocity divided by √ gh as a function of h / λ . A: phase velocity, B: group velocity, C: phase and group velocity √ gh valid in shallow water. Drawn lines: based on dispersion relation valid in arbitrary depth. Dashed lines: based on dispersion relation valid in deep water.
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,