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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:

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

Symbol	Units	Meaning
ξ	meters	Particle displacement
v	m/s	particle velocity
$ω$ = 2 · $π$ · 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
P_ac	watts	sound power or acoustic power
A	m²	Area
a	m/s&sup2	Acceleration

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Particle displacement

See also