How are loudness intensity and amplitude related?

The "loudness" of a sound is subjective, that is, it varies by the perception of the individual and cannot be measured. What is 'loud' to one person may not be to another, but increasing the amplitude will make it 'louder' to both of them.

You can measure the amplitude or sound pressure in decibels with a sound pressure level meter. Microphones and eardrums are only sensitive to the sound pressure. Forget the sound intensity.

For more, look here.

Scroll down to related inks and look at "Distance Law".