# Answer to Question #2878 in Acoustics for John

Question #2878

On the front row of the concert the sound level reaches a value of 110 dB. In the back row thw sound intensity is reduced by a factor of 1000. What is the decibel level on the back row?

Expert's answer

Decibel level defined as

L

where I

I

L

L

I

So

L

Because

L

_{1}= 10 log_{10}(I_{1}/I_{0}) dBwhere I

_{1}and I_{0}are the intensities.I

_{0}is the standard reference sound intensityL

_{1}= 10*log_{10}(I_{1}/I_{0}) = 110 dB - sound level on the front row.L

_{2}= 10*log_{10}(I_{2}/I_{0}) = 110 dB - sound level on the back row.I

_{2}=I_{1}/1000So

L

_{2}=10*log_{10}(I_{1}/1000)/I_{0}= 10*log_{10}(I_{1}/I_{0}) + 10*log_{10}(1/1000) = 110 - 3 = 107 dBBecause

**Answer : 107 dB**.
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