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 p_inst(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
P_ac	W, watts	sound power or acoustic power
A	m²	area