The intensity of the sounds that the human ear can detect

Chapter 5, Problem 47

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The intensity of the sounds that the human ear can detect varies over a very wide range of values. For instance, a whisper from 1 meter away has an intensity of approximately 1010 watts per square meter (W/m2 ), whereas, from a distance of 50 meters, the intensity of a launch of the Space Shuttle is approximately 108 W/m2 . For a sound with intensity I, the sound level b is defined by where the constant I0 is the sound intensity of a barely audible sound at the threshold of hearing. The units for the sound level b are decibels, abbreviated dB. (a) Solve the equation b 10 log10(I/I0) for I by first dividing by 10 and then converting to exponential form. (b) The sound level for a power lawnmower is b 100 db, and that for a cat purring is b 10 db. Use your result in part (a) to determine how many times more intense is the power mower sound than the cats purring. 48