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The wave equation is a second-order linear partial differential equation for the description of waves or standing wave ... for the wave equation. For velocity impulse ...
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 profile of the wave amplitudes; all transverse displacements are bound by the envelope profile.
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. For example, if a stone is thrown into the middle of a very still pond, a circular pattern of waves with a quiescent center appears in the water, also known as ...
Wave characteristics. Dispersion of gravity waves on a fluid surface. 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.
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.
where ν is the frequency of the wave, λ is the wavelength, ω = 2πν is the angular frequency of the wave, and v p is the phase velocity of the wave. The dependence of the wavenumber on the frequency (or more commonly the frequency on the wavenumber) is known as a dispersion relation.
Wave velocity is a general concept, of various kinds of wave velocities, ... The wave equation also implied the existence of a new form of matter, antimatter ...
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 dispersive waves; Signal velocity, the velocity at which a wave ...