Map A sapling learning A weather emergency siren is mounted on a tower, 165 mete

Question

Map A sapling learning A weather emergency siren is mounted on a tower, 165 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? Number How far away from the base of the tower can a person be and still be able to hear the siren? Number km Previous g Give Up & View Solution Check Answer Next D Exit Hint

Explanation / Answer

The formula for sound intensity is

beta = 10 log ( I/ I_o)

111 dB = 10 log ( I/ 1* 10 ^-12 W/m^2)

11.1 = log ( I/ 1* 10 ^-12 W/m^2)

I = 0.125 W/m^2

the relation between power and area is

p = IA = 0.125 W/m^2 ( 4 pi ( 165 m)^2 = 4.27 * 10 ^4 W

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Assuming at the max distance (R) the power has reduced to the standard threshold value 1.0^-12 W/m

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