Digital Sound & Music: Concepts, Applications, & Science, Chapter 4, last updated 6/25/2013
source. Perhaps of more practical use is the related rule of thumb that for every doubling of
distance from a sound source, you get a decrease in sound level of 6 dB. We can informally
prove the inverse square law by the following argument.
For simplification, imagine a sound as coming from a point source. This sound radiates
spherically (equally in all directions) from the source. Sound intensity is defined as sound power
passing through a unit area. The fact that intensity is measured per unit area is what is
significant here. You can picture the sound spreading out as it moves away from the source.
The farther the sound gets away from the source, the more it has “spread out,” and thus its
intensity lessens per unit area as the sphere representing the radiating sound gets larger. This is
illustrated in Figure 4.18.
Figure 4.18 Sphere representing sound radiating from a point source; radii representing two different
distances from this sound
Figure 4.19 Applying the inverse square law
This phenomenon of sound attenuation as sound moves from a source is captured in the
inverse square law, illustrated in Figure 4.20: