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 20m above the passing cars and measures a maximum intensity level of 89dB .

A) If her new home is 2.8 km

from the freeway, what's the intensity level there? Assume no decrease due to absorption by air, trees, or other objects.

B) Compare your result with a quiet whisper, 20 dB

Explanation / Answer

a)

B =beta

B=10 Log(I/Io)

89 =10 log(I/10^-12)

8.9 =log(I/10^-12)

10^8.9 =I/10^-12

I =7.94*10^-4 m^2

A =4PIR^2=4PI*20^2

A=5026.55 m^2

P=IA =7.94*10^-4*5026.66

P=3.993 Watts

when R=2.8 Km =2800 m

A=4pi*2800^2 =9.852*10^7 m^2

I=P/A =3.993/(9.852*10^7)

I=4.053*10^-8 W/m^2

B =10log(4.053*10^-8/10^-12)

B=46.08 dB

b)

SIL =46.08-20 =26.08 dB

so it louder than a quiet whisper

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