Randall D. Knight — Traveling Waves: Problem 74

The intensity of a sound source is described by an inverse-square law only if the source is very small (a point source) and only if the waves can travel unimpeded in all directions. For an extended source or in a situation where obstacles absorb or reflect the waves, the intensity at distance \(r\) can often be expressed as \(I = cP_{\text{source}}/r^x\), where \(c\) is a constant and the exponent \(x\)—which would be 2 for an ideal spherical wave—depends on the situation. In one such situation, you use a sound meter to measure the sound intensity level at different distances from a source, acquiring the data in the table. Use the best-fit line of an appropriate graph to determine the exponent \(x\) that characterizes this sound source. Data table: Distance (m) Intensity level (dB) 1 100 3 93 10 85 30 78 100 70