Adherence to and Deviation from the Inverse-Square Law of Intensity for Sound and Light

The concept of intensity—defined as power output per unit area—is often introduced when discussing sound waves and then revisited (via the Poynting vector) in discussing electromagnetic waves. The discussion is generally limited to isotropic media, with reflections and the resulting interference between waves being considered only in a limited context (such as resonances): the intensity is thus presented as obeying an inverse-square law with respect to the distance between source and observer. However, most actual demonstrations of the intensity–distance relationship (e.g., a speaker placed in a room) take place in an enclosed area, which results in reflections from the room’s boundaries (walls, ceiling, and floor) as well as from other objects in the room (desks, people, etc.). A consequence of these reflections is that the wave is no longer truly propagating in a uniform manner, but instead can interfere with its own reflections. The result of this interference is that the intensity does not ultimately follow an inverse-square law.