A rock band plays at a(n) 90-dB sound level. How many times greater is thesound

Question

A rock band plays at a(n) 90-dB sound level. How many times greater is thesound pressure from another rock band playing at each of thefollowing sound levels?

Part A asked me at 100 dB which i figured out was 10x. I knew itwas 10x because as decibels increase by a factor of 10, theintensity level is 10x. Part B asked me at 125 dB. I figured if itwas 10x from 90 to 100, so its also 10x from 100 to 120 (so20x); finally from 120 to 125 is probably 5. I added the levels and25x but it turned out to be wrong. Can someone please tell me whereI went wrong? thanks!

Explanation / Answer

Your question asks about "sound pressure," but your answer dealswith "sound intensity." I assume`they are the same (or atleast linearly related). You're right that a 10-decibel increase is a tenfold increase inintensity: 90 dB - 100 dB, 10x But, 100 - 110, 10(10x) = 100x, a hundred times the original soundintensity 110 - 120, 10(100x) = 1000x, a thousand times the original 120 - 130, 10(1000x) = 10,000x, ten thousand times theoriginal. So 125 dB is between 1000 and 10,000 times greaterin intensity. The ratio of intensities is IB/I = 10125/10/1090/10 =1012.5/109 = 103.5 ˜ 3162times greater.

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