 Particle Acceleration

# Particle acceleration

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Description:
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
[itex]
mathbf = [/itex]

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:
[itex]
mathbf = [/itex]

where
[itex]mathbf[/itex] is the average acceleration (m/s&sup2;)

[itex]mathbf[/itex] is the initial velocity (m/s)

[itex]mathbf[/itex] is the final velocity (m/s)

[itex]t[/itex] 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
[itex] mathbf = -......
...

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