Particle acceleration

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/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
<math>
mathbf = </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 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:
<math>
mathbf = </math>

where
<math>mathbf</math> is the average acceleration (m/s&sup2;)


<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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