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 18 m above the passing cars and measures a maximum intensity level of 84 dB. If her new home is 2.3 km from the freeway, what's the intensity level there? Assume no decrease due to absorption by air, trees, or other objects. Compare your result with a quiet whisper, 20 dB.

Explanation / Answer

First find the intensity using

= 10log I/Io

84 = 10logI/1 X 10-12

I = 2.52 X 10-4 W/m2

That is the intensity at 18 m, and we can find the power since I = P/A. The area is that of a surface of a sphere, which is 4r2

P = IA = (2.52 X 10-4)(4)(182) = 1.023 W

Now, find the intensity at 2.3 km (2300 m)

I = P/A = (1.023)/(4)(2300)2

I = 1.538 X 10-8 W/m2

Finally = 10log(1.538 X 10-8)/(1 X 10-12)

= 41.9 dB This is just over double the intensity level of a whisper

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