# How do you define sound intensity?

How do you define sound intensity?
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Simeon Hester
The intensity of a sound wave is determined by its amplitude. (And of course, your proximity to the source). A greater amplitude means the wave is more energetic- in terms of a sound wave an increased amplitude would mean an increased volume of the sound- which is why your ears hurt when you turn up the volume on a stereo too much. The energy transferred to your eardrum by the wave becomes painfully high.
As said, the intensity is based on amplitude, following this proportionality:
$I\propto {a}^{2}$
Where a is the amplitude of the wave (not to be confused with area)
So doubling the amplitude quadruples the intensity of the wave.
The intensity is also based on proximity to the source:
$I\propto \frac{1}{{r}^{2}}$
Where r is the distance from the source.
Which follows an inverse relationship- the further you are away from the source the less the intensity will be. Doubling your distance from the source reduces the intensity 4-fold.
This is because sound is a wave that needs a medium to travel through, its energy will dissipate over distance as energy is transferred to the air molecules.
Another definition of Intensity with a formula would be the power output per area unit:
$I=\frac{P}{A}$
$I=Intensity=W{m}^{-2}$
P=Power=(W)
$A=Area=\left({m}^{2}\right)$
Which would make sense if you placed a speaker in a small, isolated room and entered it- it sound it emitted would appear very loud.