A weather emergency siren is mounted on a tower, 177 meters above the ground. On

Question

A weather emergency siren is mounted on a tower, 177 meters above the ground. On one hand, you would like to make the siren very loud so that it will warn as many people as possible. On the other hand safety regulations prohibit you from exceeding an intensity level of 111 dB for workers standing on the ground below the siren.
Assuming the sound is uniformly emitted, what is the maximum power that the siren can put out?(W)
How far away from the base of the tower can a person still hear the siren? (KM)

Explanation / Answer

at the base we will have
use that
dB = 10 log(I/I0)
I = P/4pi r^2
111 = 10 log((P/(4*pi*105^2))/10^(-12))
solve for P, P =21656 W

at minimum hearing I = 10^(-12)
10^(-12) = 21656/(4*pi*(105^2+x^2))
x=4.15E7 m

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