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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.
The above relation between wave momentum M and wave energy density E is valid within the framework of Stokes' first definition. However, for waves perpendicular to a coast line or in closed laboratory wave channel, the second definition (S2) is more appropriate. These wave systems have zero mass flux and momentum when using the second ...
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 ...
In multidimensional systems, the wavenumber is the magnitude of the wave vector. The space of wave vectors is called reciprocal space. Wave numbers and wave vectors play an essential role in optics and the physics of wave scattering, such as X-ray diffraction, neutron diffraction, electron diffraction, and elementary particle physics.
Given the dispersion relation, one can calculate the frequency-dependent phase velocity and group velocity of each sinusoidal component of a wave in the medium, as a function of frequency. In addition to the geometry-dependent and material-dependent dispersion relations, the overarching Kramers–Kronig relations describe the frequency ...
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 profile of the wave amplitudes; all transverse displacements are bound by the envelope profile.
For a pure wave motion in fluid dynamics, the Stokes drift velocity is the average velocity when following a specific fluid parcel as it travels with the fluid flow. For instance, a particle floating at the free surface of water waves , experiences a net Stokes drift velocity in the direction of wave propagation .
A schematic diagram of a shock wave situation with the density , velocity , and temperature indicated for each region.. The Rankine–Hugoniot conditions, also referred to as Rankine–Hugoniot jump conditions or Rankine–Hugoniot relations, describe the relationship between the states on both sides of a shock wave or a combustion wave (deflagration or detonation) in a one-dimensional flow in ...