Particle Acceleration

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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

where

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

<math>mathbf</math> is the initial velocity (m/s)

<math>mathbf</math> is the final velocity (m/s)

<math>t</math> 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

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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

- <math>

where

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

This equation gives

An alternative equation is:

- <math>

where

- <math>mathbf</math> is the average acceleration (m/s²)

<math>mathbf</math> is the initial velocity (m/s)

<math>mathbf</math> is the final velocity (m/s)

<math>t</math> 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

- <math> mathbf = -...... ...

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