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

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