At a rock concert the fans in the front row are bombarded with 112 dB of sound. How many rock bands playing simultaneously at this level would be required to reach or exceed the pain threshold (120 dB)?
The answer has to be an integer. (Fractional rock bands don't exist ...)
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Let P0 be the power of one rock band. To increase from 112 dB to 120 dB requires 8 dB. The equation is
Change in dB = 10log(P1/P0)
where log is base 10. We have
8 dB = 10log(P1/P0)
0.8 = log(P1/P0)
P1/P0 = 10^0.8 = 6.30957 rock bands
Round up to 7 rock bands.
Change in dB = 10log(P1/P0)
where log is base 10. We have
8 dB = 10log(P1/P0)
0.8 = log(P1/P0)
P1/P0 = 10^0.8 = 6.30957 rock bands
Round up to 7 rock bands.
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difference is 8 dB
8 = 10 log ratio
ratio = 6.7
so 7 is your answer.
And you will get permanent hearing damage well below the pain level, somewhere around 80 dB.
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8 = 10 log ratio
ratio = 6.7
so 7 is your answer.
And you will get permanent hearing damage well below the pain level, somewhere around 80 dB.
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17