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A jet plane at take-off can produce a sound of intensity 9.70 W/m2 at 30.3 m away. But you prefer the tranquil sound of normal conversation, which is 1.0μW/m2. Assume that the plane behaves like a point source of the sound.

a. What is the closest distance you should live from the airport runway to preserve your peace of mind?
b. What intensity from the jet does your friend experience if she lives twice as far from the runway as you do?
c. What power of sound does the jet produce at take-off?

Respuesta :

Answer:

Part a)

[tex]r = 9.4 \times 10^4 m[/tex]

Part b)

[tex]I = 0.25 \mu W/m^2[/tex]

Part c)

[tex]P = 112 kW[/tex]

Explanation:

Part a)

As we know that the intensity of sound for point source is given as

[tex]I = \frac{P}{4\pi r^2}[/tex]

so here we know that

[tex]\frac{I_1}{I_2} = \frac{r_2^2}{r_1^2}[/tex]

so we have

[tex]\frac{9.70}{1\times 10^{-3}} = \frac{r^2}{30.3^2}[/tex]

[tex]r = 9.4 \times 10^4 m[/tex]

Part b)

Now we know that intensity inversely varies with the distance

So if the friend house is at double distance then the intensity must be 1/4 times

so we have

[tex]I = \frac{1 mW/m^2}{4}[/tex]

[tex]I = 0.25 \mu W/m^2[/tex]

Part c)

Power received at the time of take off is given as

[tex]\frac{P}{4\pi r^2} = 9.70 W/m^2[/tex]

[tex]r = 30.3 m[/tex]

so we have

[tex]P = 112 kW[/tex]