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Particle motion in an ocean wave at deep (A) and shallow (B) depths. 1) Propagation direction. 2) Wave crest. 3) Wave trough. Underneath the surface, there is a fluid motion associated with the free surface motion. While the surface elevation shows a propagating wave, the fluid particles are in an orbital motion.
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.
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.
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 .
The classical free particle is characterized by a fixed velocity v. The momentum is given by = and the kinetic energy (equal to total energy) by = = where m is the mass of the particle and v is the vector velocity of the particle.
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: = The relationship between the angular frequency and wavevector is called the dispersion relationship.
By comparison with vector wave equations, the scalar wave equation can be seen as a special case of the vector wave equations; in the Cartesian coordinate system, the scalar wave equation is the equation to be satisfied by each component (for each coordinate axis, such as the x component for the x axis) of a vector wave without sources of waves ...