Particle displacement
Encyclopedia : P : PA : PAR : Particle displacement
| Sound measurements |
|---|
| Sound pressure p |
| Sound pressure level (SPL) |
| Particle velocity v |
| Particle velocity level (SVL) |
| (Sound velocity level) |
| Particle displacement ξ |
| Sound intensity I |
| Sound intensity level (SIL) |
| Sound power Pac |
| Sound power level (SWL) |
| Sound energy density E |
| Sound energy flux q |
| Acoustic impedance Z |
| Speed of sound c |
Particle displacement or particle amplitude (represented in mathematics by the lower-case Greek letter ξ) is a measurement of distance (in metres) 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 oscillations of air molecules 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_ v\, \mathrmt = \int_ \frac\, \mathrmt ]
- [\xi = \frac = \frac = \frac = \frac = \frac = \frac\sqrt} = \frac\sqrt} = \frac\sqrt}}]
- [p = = ]
- [p = \frac = c \cdot \sqrt]
| Symbol | Units | Meaning |
|---|---|---|
| ξ | m, meters | Particle displacement |
| v | m/s | particle velocity |
| ω = 2πf | radians/s | angular frequency |
| f | Hz, hertz | frequency |
| p | Pa, pascals | sound pressure |
| Z = c · ρ | N·s/m3 | acoustic impedance |
| c | m/s | Speed of sound |
| ρ | kg/m3 | Density of air |
| I | W/m2 | sound intensity |
| E | W·s/m3 | sound energy density |
| Pac | W, watts | sound power or acoustic power |
| A | m2 | Area |
| a | m/s2 | Particle acceleration |
See also
External links
- [Ohm's law of the acoustics - calculations]
- [Formulas - Connection of acoustic sizes for even progressive acoustic waves - pdf]
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