Particle Velocity - Equations in Terms of Other Measurements

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

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

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
P_ac	W, watts	sound power or acoustic power
A	m²	area
a	m/s²	particle acceleration
	kg/m³	air density

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