How do you define sound intensity?
The intensity of the sound is the amplitude of the sound wave.
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:
So doubling the amplitude quadruples the intensity of the wave.
The intensity is also based on proximity to 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:
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.