# Particle acceleration

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{{short description|none}}
{{About|small-scale particle acceleration in [acoustics](/source/acoustics)|acceleration of charged particles to very high energies|particle accelerator}}
{{Multiple issues|
{{expert|physics|date=July 2024||reason=Generally unclear; also specifically not clear if referring to sound particles or matter particles. Unreferenced}}
{{One source|date=July 2024}}
{{Confusing|date=July 2018}}
}}
In [acoustics](/source/acoustics), '''particle acceleration''' is the [acceleration](/source/acceleration) (rate of change in speed and direction) of [particles](/source/particles){{clarify|date=July 2024}} in a [sound transmission](/source/sound_transmission) medium. When sound passes through a medium it causes [particle displacement](/source/particle_displacement)<ref>{{cite book
 | author= Arthur Schuster
 | title=An Introduction to the Theory of Optics
 | publisher=London: Edward Arnold
 | year=1904
 | url = https://archive.org/details/bub_gb_Zb4KAAAAIAAJ
 | quote= An Introduction to the Theory of Optics By Arthur Schuster.
 }}</ref> and as such causes changes in their acceleration.

The acceleration of the air{{dubious|date=July 2024}} particles of a [plane](/source/Plane_wave) sound wave is given by:
<math display="block">
a = \delta \cdot \omega^2 = v \cdot \omega = \frac{p \cdot \omega}{Z} = \omega \sqrt \frac{J}{Z} = \omega \sqrt \frac{E}{\rho} = \omega \sqrt \frac{P_\text{ac}}{Z \cdot A}
</math>
{| class="wikitable"
! Symbol !! Units !! Meaning
|-
! ''a''
| m/[s](/source/second)<sup>2</sup> || particle acceleration
|-
! ''v''
| [m/s](/source/Meters_per_second) || [particle velocity](/source/particle_velocity)
|-
! ''δ''
| m, meters || [particle displacement](/source/particle_displacement)
|-
! ''ω'' = 2''πf''
| [radian](/source/radian)s/[s](/source/second) || [angular frequency](/source/angular_frequency)
|-
! ''f''
| Hz, [hertz](/source/hertz) || [frequency](/source/frequency)
|-
! ''p''
| Pa, [pascal](/source/pascal_(unit))s || [sound pressure](/source/sound_pressure)
|-
! ''Z''
| [N](/source/newton_(unit))·[s](/source/second)/m<sup>3</sup> || [acoustic impedance](/source/acoustic_impedance)
|-
! ''J''
| [W](/source/Watt)/m<sup>2</sup> || [sound intensity](/source/sound_intensity)
|-
! ''E''
| [W](/source/Watt)·[s](/source/second)/m<sup>3</sup> || [sound energy density](/source/sound_energy_density)
|-
! ''P''<sub>ac</sub>
| W, [watt](/source/watt)s || [sound power](/source/sound_power) or [acoustic power](/source/acoustic_power)
|-
! ''A''
| m<sup>2</sup> || [area](/source/area)
|}

==See also==
*[Sound](/source/Sound)
*[Sound particle](/source/Sound_particle)
*[Particle displacement](/source/Particle_displacement) 
*[Particle velocity](/source/Particle_velocity)

==References==
{{reflist}}

== External links ==
*[http://www.sengpielaudio.com/RelationshipsOfAcousticQuantities.pdf Relationships of acoustic quantities associated with a plane progressive acoustic sound wave - pdf]

Category:Acoustics

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Adapted from the Wikipedia article [Particle acceleration](https://en.wikipedia.org/wiki/Particle_acceleration) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Particle_acceleration?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.