The volume control on a surround-sound amplifier is adjusted so the sound intensity level at the listening position increases from 23 to 61 dB. What is the ratio of the final sound intensity to the original sound intensity?

tarjetaroja2t 2022-09-23 Answered
The volume control on a surround-sound amplifier is adjusted so the sound intensity level at the listening position increases from 23 to 61 dB.
What is the ratio of the final sound intensity to the original sound intensity?
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Answers (1)

elilsonoulp2l
Answered 2022-09-24 Author has 9 answers
Given
β 1 = 23 d b
β 2 = 61 d b
The sound intensity level is given by
β = 10 log ( I I 0 ) where I 0 is intensity at reference level
Therefore the change in sound intensity level can be determined as
β 2 β 1 = 10 log ( I 2 I 0 ) 10 log ( I 1 I 0 )
61 23 = 10 log ( I 2 I 0 I 1 I 0 ) s i n c e log a log b = log a b
38 = 10 log ( I 2 I 1 )
3.8 = log ( I 2 I 1 )
I 2 I 1 = 10 3.8
6310
Hence
The ratio of final sound intensity to original is approximately 6310
Result:
The ratio of final sound intensity to original is approximately 6310
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