- 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::xi = int_{t} v, mathrm{d}t
If the wave is a standing wave or a traveling wave containing a single frequency, the particle displacement is::xi = frac{1}{Z} int_{t} p, mathrm{d}tThis expression for xi 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::xi = frac{v}{omega} = frac{p}{Z_0 cdot omega} = frac{a}{omega^2} = frac{1}{omega}sqrt{frac{I}{Z_0 = frac{1}{omega}sqrt{frac{E}{ ho = frac{1}{omega}sqrt{frac{P_{ac{Z_0 cdot Awhere in the above equation, the quantities xi, v, a, I, E, P_{ac} 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, Z=Z_0. Further representations for xi can be found from the above equations using the replacement omega=2pi{f}.
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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