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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 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.
Wave velocity is a general concept, of various kinds of wave velocities, for a wave's phase and speed concerning energy (and information) propagation. The phase velocity is given as: =, where: v p is the phase velocity (with SI unit m/s), ω is the angular frequency (with SI unit rad/s),
In physics, the acoustic wave equation is a second-order partial differential equation that governs the propagation of acoustic waves through a material medium resp. a standing wavefield. The equation describes the evolution of acoustic pressure p or particle velocity u as a function of position x and time t. A simplified (scalar) form of the ...
The wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields such as mechanical waves (e.g. water waves, sound waves and seismic waves) or electromagnetic waves (including light waves). It arises in fields like acoustics, electromagnetism, and fluid dynamics.
De Broglie identified the velocity of the particle, v, with the wave group velocity in free space: = (/) (The modern definition of group velocity uses angular frequency ω and wave number k ). By applying the differentials to the energy equation and identifying the relativistic momentum : p = m v 1 − v 2 c 2 {\displaystyle p={\frac {mv}{\sqrt ...
The Stokes drift velocity ū S, which is the particle drift after one wave cycle divided by the period, can be estimated using the results of linear theory: [38] u ¯ S = 1 2 σ k a 2 cosh 2 k ( z + h ) sinh 2 k h e k , {\displaystyle {\bar {\mathbf {u} }}_{S}={\tfrac {1}{2}}\sigma ka^{2}{\frac {\cosh 2k(z+h)}{\sinh ^{2}kh}}\mathbf {e ...
Sound energy density, denoted w, is defined by = where p is the sound pressure;; v is the particle velocity in the direction of propagation;; c is the speed of sound.; The terms instantaneous energy density, maximum energy density, and peak energy density have meanings analogous to the related terms used for sound pressure.