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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 ...
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,
In optics, group-velocity dispersion (GVD) is a characteristic of a dispersive medium, used most often to determine how the medium affects the duration of an optical pulse traveling through it. Formally, GVD is defined as the derivative of the inverse of group velocity of light in a material with respect to angular frequency , [ 1 ] [ 2 ]
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 ...
For the shown case, a bichromatic group of gravity waves on the surface of deep water, the group velocity is half the phase velocity. In this example, there are 5 + 3 / 4 waves between two wave group nodes in space, while there are 11 + 1 / 2 waves between two wave group nodes in time.
An acoustic waveguide is a physical structure for guiding sound waves. Sound in an acoustic waveguide behaves like electromagnetic waves on a transmission line. Waves on a string, like the ones in a tin can telephone, are a simple example of an acoustic waveguide. Another example are pressure waves in the pipes of an organ.
An atmospheric waveguide is an atmospheric flow feature that improves the propagation of certain atmospheric waves. [ 1 ] The effect arises because wave parameters such as group velocity or vertical wavenumber depend on mean flow direction and strength.