# Particle acceleration

Particle acceleration

In a compressible sound transmission medium - mainly air - air particles get an accelerated motion: the particle acceleration or sound acceleration with the symbol a in metre/second&sup2;. In acoustics or physics, acceleration (symbol: "a") is defined as the rate of change (or time derivative) of velocity. It is thus a vector quantity with dimension length/time². In SI units, this is m/s².

To accelerate an object (air particle) is to change its velocity over a period of time. Acceleration is defined technically as "the rate of change of velocity of an object with respect to time" and is given by the equation :$mathbf\left\{a\right\} = \left\{dmathbf\left\{v\right\}over dt\right\}$

where
*"a" is the acceleration vector
*"v" is the velocity vector expressed in m/s
*"t" is time expressed in seconds.

This equation gives "a" the units of m/(s·s), or m/s² (read as "metres per second per second", or "metres per second squared").

An alternative equation is::

where : is the average acceleration (m/s&sup2;)

$mathbf\left\{u\right\}$ is the initial velocity (m/s)

$mathbf\left\{v\right\}$ is the final velocity (m/s)

$t$ is the time interval (s)

Transverse acceleration (perpendicular to velocity) causes change in direction. If it is constant in magnitude and changing in direction with the velocity, we get a circular motion. For this centripetal acceleration we have:$mathbf\left\{a\right\} = - frac\left\{v^2\right\}\left\{r\right\} frac\left\{mathbf\left\{r\left\{r\right\} = - omega^2 mathbf\left\{r\right\}$

One common unit of acceleration is "g-force", one "g" being the acceleration caused by the gravity of Earth.

In classical mechanics, acceleration $a$ is related to force $F$ and mass $m$ (assumed to be constant) by way of Newton's second law: :$F = m cdot a$

Equations in terms of other measurements

The Particle acceleration of the air particles "a" in m/s² of a plain sound wave is::$a = xi cdot omega^2 = v cdot omega = frac\left\{p cdot omega\right\}\left\{Z\right\} = omega sqrt frac\left\{J\right\}\left\{Z\right\} = omega sqrt frac\left\{E\right\}\left\{ ho\right\} = omega sqrt frac\left\{P_\left\{ak\left\{Z cdot A\right\}$

ee also

* Sound pressure
* Particle displacement
* Particle velocity

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

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