Particle velocity

Particle velocity is the velocity of a particle (real or imagined) in a medium as it transmits a wave. The SI unit of particle velocity is the metre per second (m/s). In many cases this is a longitudinal wave of pressure as with sound, but it can also be a transverse wave as with the vibration of a taut string.
When applied to a sound wave through a medium of a fluid like air, particle velocity would be the physical speed of a parcel of fluid as it moves back and forth in the direction the sound wave is travelling as it passes.
Particle velocity should not be confused with the speed of the wave as it passes through the medium, i.e. in the case of a sound wave, particle velocity is not the same as the speed of sound. The wave moves relatively fast, while the particles oscillate around their original position with a relatively small particle velocity. Particle velocity should also not be confused with the velocity of individual molecules, which depends mostly on the temperature and molecular mass.
In applications involving sound, the particle velocity is usually measured using a logarithmic decibel scale called particle velocity level. Mostly pressure sensors (microphones) are used to measure sound pressure which is then propagated to the velocity field using Green's function.
Mathematical definition.
Particle velocity, denoted formula_1, is defined by
where formula_3 is the particle displacement.
Progressive sine waves.
The particle displacement of a "progressive sine wave" is given by
where
It follows that the particle velocity and the sound pressure along the direction of propagation of the sound wave "x" are given by
where
Taking the Laplace transforms of formula_15 and formula_16 with respect to time yields
Since formula_19, the amplitude of the specific acoustic impedance is given by
Consequently, the amplitude of the particle velocity is related to those of the particle displacement and the sound pressure by
Particle velocity level.
Sound velocity level (SVL) or acoustic velocity level or particle velocity level is a logarithmic measure of the effective particle velocity of a sound relative to a reference value.<br>
Sound velocity level, denoted "L""v" and measured in dB, is defined by
where
The commonly used reference particle velocity in air is
The proper notations for sound velocity level using this reference are or , but the notations , , dBSVL, or dBSVL are very common, even though they are not accepted by the SI.