Having grown tired of hearing loud music from passing cars at 3 am and the boist

Question

Having grown tired of hearing loud music from passing cars at 3 am and the boisterous yelling of bar patrons at closing, a professor buys a new home in a quiet neighborhood. She is, however, concerned about noise from freeway traffic. Using a sound intensity level meter,she stands at an overpass 17m above the passing cars and measures a maximum intensity level of 86dB .

Part A:

If her new home is 2.4km from the freeway, what's the intensity level there? Assume no decrease due to absorption by air, trees, or other objects.

Part B:

Compare your result with a quiet whisper, 20 dB.

Express your answer as an integer. Express your answer with the appropriate units.

Please answer both parts A & B

Explanation / Answer

Part A)

We first need to find the power...

Apply B = 10log(I/Io)

86 = 10log(I/(1 X 10-12)

I = 3.98 X 10-4 W/m2

Then P = IA = (3.98 X 10-4)(4pi)(17)2

P = 1.445 Watts

Next, at 2.4 km...

P = IA

1.445 = I(4pi)(2400)2

I = 2.0 X 10-8 W/m2

Finally

B = 10log(2 X 10-8)/(1 X 10-12)

B = 43 dB

Part B)

This level is just twice (2 times) the level of a whisper.

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