Considering its occurrences in various fields like Electrostatics, Gravitation, Acoustics etc. how does the law bind these topics together?
For point sources of a field or energy source, such as a charged particle, a gravitational body (which acts like a point source), or a loudspeaker on top of a tall column, the geometry of the problem controls how energy and fields distribute themselves in space. At all points that are an equal distance from a point source, the energy or field strength is constant, assuming that the point source is radiating equally in all directions. The locus of all points that are an equal distance from a point source describes a spherical surface, whose area is 4*pi*R^2, where R is the distance from the point source. If you double your distance from a point source, the sphere that has the new radius of 2R has 4 times the area of the preceding sphere, so the field or energy from the point source covers 4 times its original area, meaning that it is 1/4 the previous strength. Thus, the energy or field falls off in a 1/R^2 fashion, due to the geometry of the situation.