# Sound intensity

The sound intensity, J, (acoustic intensity) is defined as the sound power Pac per unit area A. The usual context is the measurement of sound intensity in the air at a listener's location. See the note. The SI units are watts per square metre (W/m2).

[itex]

J = \frac{1}{T} \int_{0}^{T}p(t) \cdot v(t)\,dt [itex]

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

[itex]

J_r = \frac{P_{ac}}{A} = \frac{P_{ac}}{4 \cdot \pi \cdot r^2} [itex]

The sound intensity J in W/m2 is:

[itex]

J = p \cdot v = \frac{p^2}{Z} = Z \cdot v^2 [itex]

where

J is the sound intensity, measured in watts/square metre

Pac is the acoustic power, measured in watts

p is the sound pressure, measured in Pascals (N/m2 = Pa)

v is the sound particle velocity, sound velocity or particle velocity, measured in metre per second (m/s)

Z is the acoustic impedance, measured in N·s/m3

A is the area, measured in square metres (m2)

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 is a different measure used in acoustics. Unlike sound intensity, sound intensity level is logarithmic.

Neither ear drums nor microphones can convert sound intensity to voltage modulation.

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.

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