Particle displacement
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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:
- <math>
\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}} <math>
| Symbol | Units | Meaning |
|---|---|---|
| ξ | meters | Particle displacement |
| v | m/s | particle velocity |
| <math>\omega<math> = 2 · <math>\pi<math> · 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 |