# Particle velocity

Particle velocity is the velocity of a particle(real or imagined) in a medium as it transmits a wave. 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. When applied to a sound wave through a medium of air, particle velocity would be the physical speed of an air molecule as it moves back and forth in the direction the sound wave is travelling as it passes.

Particle velocity should not be confused with the speed of the wave as it passes through the medium, i.e. in the case of a sound wave, particle velocity is not the same as the speed of sound. In applications involving sound, Particle velocity is usually measured using a logarithmic decibel scale called particle velocity level.

### Equations in terms of other measurements

[itex]

v = \xi\omega = \xi(2 \cdot \pi \cdot f) = \frac{p}{Z} = \frac{a}{\omega} = \sqrt{\frac{J}{Z}} = \sqrt{\frac{E}{\rho}} = \sqrt{\frac{P_{ac}}{Z \cdot A}} [itex]

Symbol Units Meaning
v m/s particle velocity
ξ meters Particle displacement
[itex]\omega[itex] = 2 · [itex]\pi[itex] · f radians/s angular frequency
f hertz frequency
p pascals sound pressure
Z N·s/m³ acoustic impedance
J W/m² sound intensity
E W·s/mm³ sound energy density
Pac watts sound power or acoustic power
A m² Area
a m/s&sup2 Particle acceleration

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