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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 ...
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 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.
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 the table below, several flow quantities and parameters according to Airy wave theory are given. [7] The given quantities are for a bit more general situation as for the solution given above. Firstly, the waves may propagate in an arbitrary horizontal direction in the x = (x,y) plane.
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 ...
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 ...
The potential energy in this model is given as = {, < < +,,, where L is the length of the box, x c is the location of the center of the box and x is the position of the particle within the box. Simple cases include the centered box ( x c = 0) and the shifted box ( x c = L /2) (pictured).