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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
:$$
mathbf{a} = {dmathbf{v}over dt}

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

where
: 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
:
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

Contents

Equations in terms of other measurements

See also

External links

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 = rac{p cdot omega}{Z} = omega sqrt rac{J}{Z} = omega sqrt rac{E}{
ho} = omega sqrt rac{P_{ak}}{Z cdot A}

Symbol	Units	Meaning
''a''	m/s²	particle acceleration
''v''	m/s	particle velocity
''ξ''	m, meters	particle displacement
''$omega$'' = 2 · $pi$ · ''f''	radians/s	angular frequency
''f''	Hz, hertz	frequency
''p''	Pa, pascals	sound pressure
''Z''	N·s/m³	acoustic impedance
''J''	W/m²	sound intensity
''E''	W·s/m³	sound energy density
''P''ac	W, watts	sound power or acoustic power
''A''	m²	area

See also

★ sound pressure

★ particle displacement

★ particle velocity

External links

★ Relationships of acoustic quantities associated with a plane progressive acoustic sound wave - pdf