Harman Patil (Editor)

Particle acceleration

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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. 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 = d v d t

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:

    a ¯ = v − u t

    where

    a ¯ is the average acceleration (m/s2)

    u is the initial velocity (m/s)

    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

    a = − v 2 r r r = − ω 2 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 ⋅ 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 = δ ⋅ ω 2 = v ⋅ ω = p ⋅ ω Z = ω J Z = ω E ρ = ω P a c Z ⋅ A

    References

    Particle acceleration Wikipedia
    (Text) CC BY-SA