The Inverse Square Law

In the "free field" (meaning in the absence of obstacles that might interfere with wave propagation), sound waves will spread out in all directions, like spheres radiating out from the source at the speed of sound.

Clearly, as the radius of the spheres gets larger, the amount of acoustic energy in the sound gets "stretched thinner and thinner" over the expanding surface of the sphere. Given that the surface of a sphere is proportional to the square of its radius (A = 4⋅π⋅r2), the energy in the sound wave that would impinge on a fixed small area (e.g. an ear drum) therefore declines with the square of the distance from the source.

This relationship between sound intensity and distance from the source is known as the inverse square law.

Note that in closed rooms where considerable amounts of sound energy may be reflected back from walls, floor or ceiling, the inverse square law usually does not hold.

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