Sound Intensity - Acoustic Intensity

Acoustic Intensity

The intensity is the product of the sound pressure and the particle velocity

\vec{I} = p \vec{v}

Notice that both v and I are vectors, which means that both have a direction as well as a magnitude. The direction of the intensity is the average direction in which the energy is flowing. For instantaneous acoustic pressure pinst(t) and particle velocity v(t) the average acoustic intensity during time T is given by

I = \frac{1}{T} \int_{0}^{T}p_\mathrm{inst}(t) v(t)\,dt

The SI units of intensity are W/m2 (watts per square metre). For a plane progressive wave we have:

I = \frac{p^2}{Z} = Z v^2 = \xi^2 \omega^2 Z = \frac{a^2 Z}{\omega^2} = E c = \frac{P_{ac}}{A}

where:

Symbol Units Meaning
p pascals RMS sound pressure
f hertz frequency
ξ m, metres particle displacement
c m/s speed of sound
v m/s particle velocity
ω = 2πf radians/s angular frequency
ρ kg/m3 density of air
Z = c ρ N·s/m³ characteristic acoustic impedance
a m/s² particle acceleration
I W/m² sound intensity
E W·s/m³ sound energy density
Pac W, watts sound power or acoustic power
A m² area

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