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. 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:
- is the average acceleration (m/s²)
is the initial velocity (m/s)
is the final velocity (m/s)
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
Equations in terms of other measurements
The Particle acceleration of the air particles a in m/s² of a plain sound wave is:
|δ||m, meters||particle displacement|
|= 2 · · f||radians/s||angular frequency|
|p||Pa, pascals||sound pressure|
|E||W·s/m³||sound energy density|
|Pac||W, watts||sound power or acoustic power|