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If the intensity increased by a factor o...

If the intensity increased by a factor of 20, byhow may decibels is the sound level increased?

A

18

B

13

C

9

D

7

Text Solution

Verified by Experts

The correct Answer is:
B
Suppose for the intensity `I`, the correspongind decibel level is `beta_(1)`. When the intensity is increased to `20I`, then corresponding increase in decibels level be `beta_(2)`.
Then`beta_(1)=10log(I//I_(0))`
and `beta_(2)=10 log (20I//I_(0))`
`:.beta_(2)-beta_(1)=10log(20I//I_(0))-10log(I//I_(0))`
`=10log (20I//I)=10log 20`
`=10xx1.3142=13.142dB~~13dB`
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