Answer to Question #2878 in Acoustics for John

Question

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?

Answer 1

Decibel level defined as

L₁ = 10 log₁₀(I₁/I₀) dB

where I₁ and I₀ are the intensities.
I₀ is the standard reference sound intensity

L₁ = 10*log₁₀ (I₁/I₀) = 110 dB - sound level on the front row.
L₂ = 10*log₁₀ (I₂/I₀) = 110 dB - sound level on the back row.
I₂=I₁/1000
So
L₂=10*log₁₀ (I₁/1000)/I₀ = 10*log₁₀(I₁/I₀) + 10*log₁₀(1/1000) = 110 - 3 = 107 dB
Because
Answer : 107 dB.