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Particle displacement or '''particle amplitude''' (represented in Mathematics by the Lower-case Greek Letter ξ ) is a Measurement of Distance (in Metre s) of the movement of a particle in a medium as it transmits a Wave . In most cases this is a Longitudinal Wave of pressure (such as Sound ), but it can also be a Transverse Wave , such as the Vibration of a taut string. In the case of a Sound Wave travelling through Air , the '''particle displacement''' is evident in the Oscillation s of air Molecule s of air in and against the direction in which the sound wave is travelling with the Speed Of Sound with 343 m/s at 20 °C.

Particle displacement ''ξ'' in m for a plane wave is:
:
\xi = \int_{t} v\, \mathrm{d}t = \int_{t} rac{p}{Z}\, \mathrm{d}t


Particle displacement can be represented in terms of other measurements:
:
\xi = rac{v}{\omega} = rac{v}{2 \cdot \pi \cdot f} = rac{p}{Z \cdot \omega} = rac{p}{Z \cdot 2 \cdot \pi \cdot f} = rac{a}{\omega^2} = rac{1}{\omega}\sqrt{ rac{I}{Z}} = rac{1}{\omega}\sqrt{ rac{E}{ ho}} = rac{1}{\omega}\sqrt{ rac{P_{ac}}{Z \cdot A}}


We get for the sound pressure ''p'':
:
p = {\xi \cdot Z \cdot \omega} = {\xi \cdot Z \cdot 2 \cdot \pi \cdot f}

:
p = rac{a \cdot Z}{\omega} = c \cdot \sqrt{ ho \cdot E}


where:


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