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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.
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.
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 ]
In general, for a waveguide mode with an angular frequency ω(β) at a propagation constant β (so that the electromagnetic fields in the propagation direction z oscillate proportional to e i(βz−ωt)), the group-velocity dispersion parameter D is defined as [5]
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 ...
A waveguide is a structure that guides waves by restricting the transmission of energy to one direction. Common types of waveguides include acoustic waveguides which direct sound, optical waveguides which direct light, and radio-frequency waveguides which direct electromagnetic waves other than light like radio waves.
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.
Dispersion of gravity waves on a fluid surface. Phase and group velocity divided by shallow-water phase velocity √ gh as a function of relative depth h / λ. Blue lines (A): phase velocity; Red lines (B): group velocity; Black dashed line (C): phase and group velocity √ gh valid in shallow water.