Particle acceleration

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}

*"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::mathbf{ar{a = {mathbf{v} - mathbf{u} over t}

where :mathbf{ar{a 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

* [ Relationships of acoustic quantities associated with a plane progressive acoustic sound wave - pdf]

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