Sound intensity
Categories: Sound | Acoustics | Physical quantity
The sound intensity, I, (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 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 \cdot \pi \cdot 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
p is the sound pressure, measured in Pascals (N/m2 = Pa)
v is the sound particle velocity, sound velocity or particle velocity, measured in m/s (metres per second)
Z is the acoustic impedance, measured in N·s/m3
ξ is the particle displacement of the air particles, measured in m
<math>\pi</math> is the angular frequency = 2 <math>\pi</math> · f measured in Hz
I is the sound intensity, measured in watts/m2 (watts per square metre)
Pac is the acoustic power, measured in watts
A is the area, measured in m2
a is the particle acceleration measured in m/s2 (metres per square second)
E is the sound energy density measured in W·s/m3
c is the sound speed measured in m/s
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.
Sound intensity is never sound pressure. Ears are sensitive to sound pressure only and insensitive to sound intensity.
Sound measurements
- Sound pressure
- Sound pressure level (SPL)
- Particle velocity
- Particle velocity level (sometimes called Sound velocity level) (SVL)
- Particle displacement
- Sound intensity
- Sound intensity level (SIL)
- Sound power
- Sound power level (SWL)
- Sound energy flux
- Acoustic impedance
- Speed of sound