A jet plane at take-off can produce sound of intensity 10.0 W/m^2 at 30.0 m away

Question

A jet plane at take-off can produce sound of intensity 10.0 W/m^2 at 30.0 m away. But you prefer the tranquil sound of normal conversation, which is 1.0 mu W/m^2 Assume that the plane behaves like a point source of sound. What is the closest distance you should live from the airport runway to preserve your peace of mind? Express your answer using two significant figures. r = What intensity from the jet does your friend experience if she lives twice as far from the runway as you do? Express your answer using two significant figures. I =

Explanation / Answer

Given,

I1 = 10 W/m^2 ; r1 = 30 m ; I2 = 1 x 10^-6 W/m^2

A)Let the required distance be r2.

We know that intensi is given by

I = P/A = P/4 pi r^2

I1 = P/4 pi r1^2 ; I2 = P/4 pi r2^2

I1/I2 = r2^2/r1^2 = (r2/r1)^2

r2 = r1 x sqrt (I1/I2)

r2 = 30 x sqrt (10/10^-6) = 94.87 x 10^3 m = 94.87 km

Hence, r2 = 94.87 km (upto two sig fig.)

B)R2 = 2 x 94.87 km = 189.74 km

I1 = P/4 pi r1^2 ; I2 = P/4 pi r2^2

I1/I2 = r2^2/r1^2

I2 = (r1/r2)^2 I1

I2 = (94.87/189.74)^2 10^-6 = 0.25 x 10^-6 W/m^2

Hence, I2 = 0.25 u W/m^2

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