sound intensity
Stand close to a speaker and the sound pours over you, step far away and it fades. Sound intensity measures how much sound energy flows through each patch of area every second, how concentrated the sound is. The question it answers is: how do we put a number on how much sound energy reaches a spot?
Sound intensity I is the power carried by the wave divided by the area it passes through: I = P / A, measured in watts per square metre (W/m^2). For a small source radiating equally in all directions, the same power spreads over an ever-bigger sphere as you move away, so the intensity falls off as the inverse square of distance: I is proportional to 1 / r^2, double the distance and you get one-quarter the intensity. The intensity also grows with the square of the wave's amplitude.
Human hearing spans an enormous range of intensities, from the faintest audible sound at about I_0 = 10^-12 W/m^2 (the threshold of hearing) up to the pain threshold near 1 W/m^2, a range of a trillion to one. That huge span is exactly why we compress it onto the logarithmic decibel scale. An honest note: intensity (a physical flow of energy) is not the same as loudness (how loud it seems to you), the ear's sensitivity depends on frequency, so equal intensities at different pitches do not sound equally loud.
A point source radiating P = 0.1 W of sound equally in all directions gives, at r = 2 m, an intensity I = P/(4 pi r^2) = 0.1/(4 pi times 4), about 0.002 W/m^2. Move to 4 m and it drops to a quarter of that.
Intensity is power per area; for a point source it falls as 1/r^2.
Intensity is measured energy flow, not perceived loudness. The ear hears some frequencies more easily than others, so equal intensity does not mean equal loudness.