Particle velocity

Sound measurements
Characteristic
Symbol
Sound pressure  p · SPL
Particle velocity  v · SVL
Particle displacement  ξ
Sound intensity  I · SIL
Sound power  Pac
Sound power level  SWL
Sound energy
Sound exposure  E
Sound exposure level  SEL
Sound energy density  E
Sound energy flux  q
Acoustic impedance  Z
Speed of sound
Audio frequency  AF

Particle velocity is the velocity v of a particle (real or imagined) in a medium as it transmits a wave. 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.

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. Only since recent years it is possible to directly measure particle velocity with a Microflown sensor.

Equations in terms of other measurements

The velocity v can be related to the particle displacement $\xi$ and acceleration for single frequency plane wave of frequency f using

$v = \xi\cdot \omega = \xi(2 \pi f) = \frac{p}{Z} = \frac{a}{\omega} = \sqrt{\frac{E}{\rho}} = \sqrt{\frac{P_{ac}}{Z \cdot A}}$

It is further related to the instantaneous acoustic intensity vector I (not the time-averaged acoustic intensity) according to

$v = \frac{I}{p}$
Symbol Units Meaning
v m/s particle velocity
ξ m, meters particle displacement
ω = 2πf radians/s angular frequency
f Hz, hertz frequency
p Pa, pascals sound pressure
Z N·s/m³ acoustic impedance
E W·s/m³ sound energy density
Pac W, watts sound power or acoustic power
A area
a m/s² particle acceleration
$\rho$ kg/m³ air density

Particle velocity level

The particle velocity level or the sound velocity level tells the ratio of a sound incidence in comparison to a reference level of 0 dB in a medium, mostly air.

It shows the ratio of the particle velocity v1 and the particle velocity v0.

The particle velocity level is:

$L_v = 20\, \log_{10}\left(\frac{v_1}{v_0}\right) \mathrm{dB}$

where v1 and v0 are the velocities.

The particle velocity level has the letter "Lv".

The unit of the particle velocity level is named "dB".

Notice: The dB is dimensionless.

If v0 is the standard reference particle velocity of:[citation needed]

$v_0 = 5.0 \times 10^{-8} \mathrm{\frac{m}{s}}$

we use "dB SVL". (SVL = sound velocity level).

Sound particle velocity v should not be confused with Sound velocity c.