SAT Subject Physics Practice Question 114: Answer and Explanation
9. An observer is 2 m from a source of sound waves. By how much will the sound level decrease if the observer moves to a distance of 20 m ?
A. 1 dB
B. 2 dB
C. 10 dB
D. 18 dB
E. 20 dB
Correct Answer: E
The intensity (power per unit area) is proportional to 1/r2, where r is the distance between the source and the detector. If r increases by a factor of 10, the intensity decreases by a factor of 100. Because the decibel scale is logarithmic, if the intensity decreases by a factor of 100 = 102, the decibel level decreases by 10 log (102) = 20 dB.