- Particle displacement
Particle displacement or particle amplitude (represented in
mathematics by the lower-case Greek letter ξ) is ameasurement ofdistance (inmetre s) of the movement of a particle in a medium as it transmits awave . In most cases this is alongitudinal wave of pressure (such assound ), but it can also be atransverse wave , such as the vibration of a taut string. In the case of asound wave travelling throughair , the particle displacement is evident in theoscillation s of airmolecule s with, and against, the direction in which the sound wave is travelling. A particle of the medium undergoes displacement according to theparticle velocity of the wave traveling through the medium, while the sound wave itself moves at thespeed of sound , equal to 343 m/s in air at 20 °C.The instantaneous particle displacement "ξ" in m for a wave is::
If the wave is a standing wave or a traveling wave containing a single frequency, the particle displacement is::This expression for undergoes simple harmonic oscillation, and as such is usually expressed as an
rms time average.Particle displacement for a traveling wave containing a single frequency can be represented in terms of other measurements::where in the above equation, the quantities may be taken throughout as rms time-averages (or all as maximum values). The single frequency traveling wave has acoustic impedance equal to the characteristic impedance, . Further representations for can be found from the above equations using the replacement .
See also
*
Wave
*Sound particle External links
* [http://acoustics.open.ac.uk/pdf/ali_tonddast_navaei_thesis.pdf Acoustic particle-image velocimetry - Development and applications]
* [http://www.sengpielaudio.com/calculator-ak-ohm.htm Ohm's law as acoustic equivalent - calculations]
* [http://www.sengpielaudio.com/RelationshipsOfAcousticQuantities.pdf Relationships of acoustic quantities associated with a plane progressive acoustic sound wave - pdf]
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