Loudness and intensity

The increase in loudness is proportional to the fractional change in intensity or:

If the intensity of a sound doubles and then doubles again the loudness will increase by the same amount each time.

where I_o is the threshold intensity, or initial intensity, and k and C are constants. For example if the intensity of a sound goes up from say 2x10^-8 Wm^-2 to 4x10^-8 Wm^-2 and then increases again from 4x10^-8 Wm^-2 to 8x10^-8 Wm^-2 the loudness will increase by a factor of 2 each time.