- 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
acousticsor 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 :
*"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)
is the initial velocity (m/s)
is the final velocity (m/s)
is the time interval (s)
Transverseacceleration (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 accelerationwe have:
One common unit of acceleration is "
g-force", one "g" being the acceleration caused by the gravity of Earth.
classical mechanics, acceleration is related to force and mass(assumed to be constant) by way of Newton's second law: :
Equations in terms of other measurements
The Particle acceleration of the air particles "a" in m/s² of a plain sound wave is::
* [http://www.sengpielaudio.com/RelationshipsOfAcousticQuantities.pdf Relationships of acoustic quantities associated with a plane progressive acoustic sound wave - pdf]
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