Sound intensity

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The sound intensity, I, (acoustic intensity) is defined as the sound power P_ac per unit area A. The usual context is the measurement of sound intensity in the air at a listener's locationTemplate:Ref. The SI units are W/m² (watts per square metre).

<math>

I = \frac{1}{T} \int_{0}^{T}p(t) \cdot v(t)\,dt </math>

For a spherical sound source, the intensity as a function of distance r is:

<math>

I_r = \frac{P_{ac}}{A} = \frac{P_{ac}}{4 \pi r^2} </math>

The sound intensity I in W/m² of a plane progressive wave is:

<math>

I = p \cdot v = \frac{p^2}{Z} = Z \cdot v^2 = \xi^2 \cdot \omega^2 \cdot Z = \frac{a^2 \cdot Z}{\omega^2} = E \cdot c = \frac{P_{ac}}{A} </math>

where:

Symbol	Units	Meaning
p	pascals	sound pressure
f	hertz	frequency
ξ	m, meters	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	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

The amplitude of sound intensity (not sound pressure!) decreases in the free field (direct field) with 1/r² of the distance of a point source.

Sound intensity level, L_I, is the sound intensity, expressed in logarithmic units.

<math>L_I=10 \log_{10} \frac {I}{I_o}</math> (dB-SIL),

where I_o is the reference intensity, 10^-12 W/m²

Note 1Template:Note: The term "intensity" is used exclusively for the measurement of sound in watts per unit area. To describe the strength of sound in terms other than strict intensity, one can use "magnitude" "strength", "amplitude", or "level" instead.

Sound intensity is not the same physical quantity as sound pressure. Hearing is directly sensitive to sound pressure which is related to sound intensity.

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