weather emergency siren is mounted on a tower, 165 meters above the ground. On o

Question

weather emergency siren is mounted on a tower, 165 meters above the ground. On one hand, you ould 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 101 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 4307.0285 How far away from the base of the tower can a person be and still be able to hear the siren? Number Incorrect. Express your answer in the requested units. 1.85 x 107 km

Explanation / Answer

Sound level intensity is given by:

SL = 10*log (I/I0)

I0 = 10^-12 W/m^2

given that SL = 101 dB

101 = 10*log (I/I0)

I/I0 = 10^(10.1)

I = 10^-12*10^(10.1)

I = 0.0126 W/m^2

We know that

P = I*A

P = I*4*pi*R^2

P = 0.0126*4*pi*165^2 = 4310.7 W

B.

Person can hear the siren till the intensity drops to 10^-12 W/m^2, So

P = I0*A = I0*4*pi*R^2

R = sqrt (P/(I0*4*pi))

R = sqrt (4310.7/(4*pi*10^-12))

R = 1.85*10^7 m = 1.85*10^4 km

You need to answer in km, your input answer is in m

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