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 17 m above the passing cars and measures a maximum intensity level of 87 dB .

If her new home is 2.2 km from the freeway, what's the intensity level there? Assume no decrease due to absorption by air, trees, or other objects.

Explanation / Answer

Intensity level is beta = 10 dB*log(I/Io)

Io = 10^-12 W/m^2

87dB = 10 dB*log(I/10^-12)

8.7 = log*(I/10^-12)

I/10^-12 = 10^8.7 =

I = 5.011*10^-4 W/m^2

but I1*r1^2 = I2*r2^2

5.011*10^-4*17*17 = I2*2200*2200

I2 = 2.99*10^-8 W/m^2

then intensity level is beta = 10dB*log(I/Io) = 10 dB*log(2.99*10^-8/10^-12) = 44.75 dB

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