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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 notion of group velocity is based on a linear approximation to the dispersion relation () near a particular value of . [6] In this approximation, the amplitude of the wave packet moves at a velocity equal to the group velocity without changing shape. This result is an approximation that fails to capture certain interesting aspects of the ...
In a sound wave, the complementary variable to sound pressure is the particle velocity. Together, they determine the sound intensity of the wave. Sound intensity, denoted I and measured in W·m −2 in SI units, is defined by =, where p is the sound pressure, v is the particle velocity.
In dispersive media the phase velocity is not necessarily the same as the group velocity. 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 ...
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 ...
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),
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 ...
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 has twice the momentum, while the bottom electron ...