# 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/second². Inacoustics orphysics ,**acceleration**(symbol: "a") is defined as the rate of change (or timederivative ) ofvelocity . It is thus a vector quantity with dimensionlength /time ². 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 :$mathbf\{a\}\; =\; \{dmathbf\{v\}over\; dt\}$

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::$mathbf\{ar\{a\; =\; \{mathbf\{v\}\; -\; mathbf\{u\}\; over\; t\}$

where :$mathbf\{ar\{a$ is the average acceleration (m/s²)

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

$mathbf\{v\}$ 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 acircular motion . For thiscentripetal acceleration we have:$mathbf\{a\}\; =\; -\; frac\{v^2\}\{r\}\; frac\{mathbf\{r\{r\}\; =\; -\; omega^2\; mathbf\{r\}$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 $F$ andmass $m$ (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::$a\; =\; xi\; cdot\; omega^2\; =\; v\; cdot\; omega\; =\; frac\{p\; cdot\; omega\}\{Z\}\; =\; omega\; sqrt\; frac\{J\}\{Z\}\; =\; omega\; sqrt\; frac\{E\}\{\; ho\}\; =\; omega\; sqrt\; frac\{P\_\{ak\{Z\; cdot\; A\}$**ee also***

Sound pressure

*Particle displacement

*Particle velocity **External links*** [

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

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