As a result, the sound intensity follows an inverse square law. As you get farther and farther from the source, the power put out by the sound source gets spread over a larger and larger area. Sound radiating into open space works the same way. In math speak, the concentration of the paint follows an inverse square law. At triple the initial distance, the paint spot has nine times the original size and the paint is only one ninth as thick, and so on.

As a result, the paint is only one quarter as thick as before. Since the new paint spot is bothtwice as wide andtwice as high as the original, it covers four times the area. What did you answer? Twice the area? Half as thick? If you did, you got the answers wrong! Remember that area is length times width. How much larger is the new spot? How thick is the paint? You then deliver the same dose of paint from twice as far away and compare. Suppose you squirt a dose of paint on a wall. Hold the can further away and the same amount of paint gives a thinner coat that covers a larger area. Hold the can close to the surface you’re painting, you get a small spot of really thick paint. If you’ve ever used a can of spray paint, you know that distance is important- the closer you are to the nozzle, the more concentrated the paint stream is. Inverse square law and the paint can analogy Unless there are surfaces for the sound to reflect from, the sound’s intensity becomes less and less as you get further from the source. Much like light, sound spreads out as it travels away from the source. Loudness perception 45 Intensity and Distance Intensity and distanceĪs you move away from a sound source, the sound gets quieter- especially when you are outdoors.

Inverse fourth power law