# Particle displacement

Particle displacement or particle amplitude ξ is a distance measurement in m (metre) of the movement of a particle(real or imagined) in a medium as it transmits a wave. In most 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 displacement would be the physical movement back and forth of a molecule of air in the direction the sound wave is travelling as it passes.

It can be represented in terms of other measurements:

[itex]

\xi = \frac{v}{\omega} = \frac{v}{2 \cdot \pi \cdot f} = \frac{p}{Z \cdot \omega} = \frac{p}{Z \cdot 2 \cdot \pi \cdot f} = \frac{a}{\omega^2} = \frac{1}{\omega}\sqrt{\frac{J}{Z}} = \frac{1}{\omega}\sqrt{\frac{E}{\rho}} = \frac{1}{\omega}\sqrt{\frac{P_{ac}}{Z \cdot A}} [itex]

Symbol Units Meaning
ξ meters Particle displacement
v m/s particle velocity
[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/m³ sound energy density
Pac watts sound power or acoustic power
A m² Area
a m/s² Acceleration

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