A weather emergency siren is mounted on a tower, 189 meters above the ground. On

Question

A weather emergency siren is mounted on a tower, 189 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 116 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?

How far away from the base of the tower can a person be and still be able to hear the siren? Neglect any absorption of sound energy by the air, though in reality such absorption would be significant at long distances.

Question 13 of 19 Map cro sapling leaming ground directily below ther siren .rom exceeding an itesit leve of 116 ds for workers standing on the A weather emergency siren is mounted on a tower, 189 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 116 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? Neglect any absorption of sound energy by the air, though in reality such absorption would be significant at long distances. Number Im - O Previous Give Up & View Solution O Check Answer 0 Next Next Exit Exit Hint

Explanation / Answer

Let P is the power of siren and I is theintensity of the siren.

A) at a point directly below the tower

sount inetsnity level, beta = 10*log(I/Io)

106 = 10*log(I/10^-12)

10.6 = log(I/10^-12)

10^10.6 = I/10^12

I = 10^(10.6 - 12)

= 0.0398 W/m^2

we know, Power output = Intensity*Area

= 0.0398*4*pi*r^2

= 0.0398*4*pi*189^2

= 17866 W <<<<<<<<<---------Answer

minimum intensity of sound that is sensible to hear = 10^-12 W/m^2

let d is the distance from the tower where a person hears minimum sound.

I_min = P/(4*pi*d^2)

d^2 = P/(4*pi*I_min)

d = sqrt(P/(4*pi*I_min))

= sqrt(17866/(4*pi*10^-12))

= 37705840 m

so, distance from the base = sqrt(37705840^2 - 189^2)

= 37705840 m <<<<<<<<<---------Answer

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