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. 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 :$mathbf\{a\}\; =\; \{dmathbf\{v\}over\; dt\}$

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::

where : 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 a circular motion. For this centripetal 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 $F$ 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::$a\; =\; xi\; cdot\; omega^2\; =\; v\; cdot\; omega\; =\; frac\{p\; cdot\; omega\}\{Z\}\; =\; omega\; sqrt\; frac\{J\}\{Z\}\; =\; omega\; sqrt\; frac\{E\}\{\; ho\}\; =\; omega\; sqrt\; frac\{P\_\{ak\{Z\; cdot\; A\}$

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]