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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.
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 ...
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.
The deep-water wavelength is L 0 = g/(2π)T 2 and the deep-water phase speed is c 0 = L 0 /T. The grey line corresponds with the shallow-water limit c p =c g = √(gh). The phase velocity c p is related to the wavelength L through c p = L/T. Consequently, for fixed period T, L/L 0 varies identical to c p /c 0 with depth changes.
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 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]
The group velocity ∂Ω / ∂k of capillary waves – dominated by surface tension effects – is greater than the phase velocity Ω / k . This is opposite to the situation of surface gravity waves (with surface tension negligible compared to the effects of gravity) where the phase velocity exceeds the group velocity. [13]
Animation: phase and group velocity of electrons This animation portrays the de Broglie phase and group velocities (in slow motion) of three free electrons traveling over a field 0.4 ångströms in width. The momentum per unit mass (proper velocity) of the middle electron is lightspeed, so that its group velocity is 0.707 c. The top electron ...