A weather emergency siren is mounted on a tower, 141 meters above the ground. On

Question

A weather emergency siren is mounted on a tower, 141 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 directly below the siren. Assuming that the sound is uniformly emitted, what is the maximum power that the siren can put out? And how far away can someone be from the tower and still hear it?

Explanation / Answer

111 = 10*logI1/Io

I1 = 1.26*10^11*Io = 0.126 w/m^2

#a) P = I1*(4*pi*r1^2)

P = 0.126*(4*3.14*153*153) = 37046.14704 W

#b) at far point I2 = Io = 10^-12 W/m^2

I2 = P/4*pi*r2^2

r2 = 5.431e7 m

so x = sqrt(r1^2+r2^2)

x = 5.43*10^7 m <----------answer

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