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Particle velocity (denoted v or SVL) is the velocity of a particle (real or imagined) in a medium as it transmits a wave. The SI unit of particle velocity is the metre per second (m/s). In many cases this is a longitudinal wave of pressure as with sound , but it can also be a transverse wave as with the vibration of a taut string.
In the de Broglie hypothesis, the velocity of a particle equals the group velocity of the matter wave. [ 2 ] : 214 In isotropic media or a vacuum the group velocity of a wave is defined by: v g = ∂ ω ( k ) ∂ k {\displaystyle \mathbf {v_{g}} ={\frac {\partial \omega (\mathbf {k} )}{\partial \mathbf {k} }}} The relationship between the ...
When following a single particle in pure wave motion (U = 0), according to linear Airy wave theory, a first approximation gives closed elliptical orbits for water particles. [36] However, for nonlinear waves, particles exhibit a Stokes drift for which a second-order expression can be derived from the results of Airy wave theory (see the table ...
A wave with the group and phase velocities going in different directions. Group velocity is a property of waves that have a defined envelope, measuring propagation through space (that is, phase velocity) of the overall shape of the waves' amplitudes—modulation or envelope of the wave.
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 ...
If a travelling wave is reflected, the reflected wave can interfere with the incident wave causing a standing wave in the near field. As a consequence, the local pressure in the near field is doubled, and the particle velocity becomes zero. Attenuation causes the reflected wave to decrease in power as distance from the reflective material ...
For high frequencies and modes have the Rayleigh wave velocity, approximate 92 % of the shear wave velocity. Lamb waves exhibit velocity dispersion; that is, their velocity of propagation c depends on the frequency (or wavelength), as well as on the elastic constants and density of the material.
If the momentum of the initial wave function is highly localized, the wave packet will spread slowly and the group-velocity approximation will remain good for a long time. Intuitively, this result says that if the initial wave function has a very sharply defined momentum, then the particle has a sharply defined velocity and will (to good ...