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{{Sound measurements}}
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'''Particle velocity''' is the velocity ''v'' of a particle (real or imagined) in a [[Transmission medium|medium]] as it transmits a [[wave]]. In many 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 a fluid like air, particle velocity would be the physical speed of a parcel of fluid as it moves back and forth in the direction the sound wave is travelling as it passes.
 
Particle velocity should not be confused with the speed of the [[wave]] as it passes through the medium, i.e. in the case of a sound wave, particle velocity is not the same as the [[speed of sound]]. The wave moves relatively fast, while the particles oscillate around their original position with a relatively small particle velocity. Particle velocity should also not be confused with the velocity of individual molecules.  
 
In applications involving sound, the particle velocity is usually measured using a logarithmic [[decibel]] scale called [[particle velocity level]].
 
== Equations in terms of other measurements ==
The velocity '''v''' can be related to the particle displacement <math>\xi</math> and acceleration for single frequency plane wave of frequency f using
:<math>
v = \xi\cdot \omega = \xi(2 \pi f) = \frac{p}{Z} = \frac{a}{\omega} = \sqrt{\frac{E}{\rho}} = \sqrt{\frac{P_{ac}}{Z \cdot A}}
</math>
 
It is further related to the ''instantaneous'' acoustic intensity vector '''I''' (not the time-averaged [[acoustic intensity]]) according to
 
:<math>
v = \frac{I}{p}
</math>
 
{| class="wikitable"
! Symbol !! Units !! Meaning
|-
! ''v''
| [[Meters per second|m/s]] || particle velocity
|-
! ''ξ''
| m, meters || [[particle displacement]]
|-
! ''ω'' = 2''πf''
| [[radian]]s/[[second|s]] || [[angular frequency]]
|-
! ''f''
| Hz, [[hertz]] || [[frequency]]
|-
! ''p''
| Pa, [[pascal (unit)|pascal]]s || [[sound pressure]]
|-
! ''Z''
| [[Newton (unit)|N]]·[[second|s]]/m³ || [[acoustic impedance]]
|-
! ''E''
| [[Watt|W]]·[[second|s]]/m³ || [[sound energy density]]
|-
! ''P''<sub>ac</sub>
| W, [[watt]]s || [[sound power]] or [[acoustic power]]
|-
! ''A''
| m² || [[area]]
|-
! ''a''
| m/[[second|s]]² || [[particle acceleration]]
|-
! ''<math>\rho</math>''
| kg/[[m]]³ || [[air density]]
|}
 
==Particle velocity level==
The '''particle velocity level''' or the '''sound velocity level''' tells the ratio of a sound incidence in comparison to a reference level of 0 dB in a medium, mostly air.
 
It shows the ratio of the particle velocity ''v''<sub>1</sub> and the particle velocity ''v''<sub>0</sub>.
 
The '''particle velocity level''' is:
:<math>
L_v = 20\, \log_{10}\left(\frac{v_1}{v_0}\right) \mathrm{dB}
</math>
 
where ''v''<sub>1</sub> and ''v''<sub>0</sub> are the velocities.
 
The particle velocity level has the letter "''L''<sub>v</sub>".
 
The [[Units of measurement|unit]] of the particle velocity level is named "dB".
 
Notice: The [[decibel|dB]] is dimensionless.
 
If ''v''<sub>0</sub> is the standard reference particle velocity of:{{fact|date=January 2013}}
:<math>
v_0 = 5.0 \times 10^{-8} \mathrm{\frac{m}{s}}
</math>
 
we use "dB SVL". (SVL = sound velocity level).
 
[[Sound particle velocity]] ''v'' should not be confused with [[Sound velocity]] ''c''.
 
== See also ==
*[[Sound particle]]
*[[Particle displacement]]
*[[Particle acceleration]]
*[[Pressure gradient]]
 
== External links ==
*[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]
*[http://www.microflown.com The particle velocity can be directly measured with a Microflown]
*[http://acoustics.open.ac.uk/pdf/ali_tonddast_navaei_thesis.pdf Acoustic particle-image velocimetry - development and applications]
 
[[Category:Fluid dynamics]]
[[Category:Sound measurements]]

Latest revision as of 18:03, 27 May 2014

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