   Chapter 14, Problem 73AP

Chapter
Section
Textbook Problem

An interstate highway has been built through a neighborhood in a city. In the afternoon, the sound level in an apartment in the neighborhood is 80.0 dB as 100 cars pass outside the window every minute. Late at night, the traffic flow is only five cars per minute. What is the average late-night sound level?

To determine
The average late night sound level in the traffic flow area.

Explanation

Given Info: The sound level in an apartment in the neighborhood is 80.0dB .

Let us consider that the average intensity of the sound is directly proportional to the number of cars passing in each minute.

Formula to calculate the sound level in decibels is,

β=10log(II0)

• β is the sound level in an apartment,
• I is the intensity of the sound,
• I0 is the reference intensity,

Rewrite the above relation for average intensity in the afternoon, when 100 cars passing in terms of I100cars .

I100cars=I010β/10

Substitute 1012W/m2 for I0 and 80.0dB for β , we get I100cars .

I100cars=(1012W/m2)1080.0/10=(1012W/m2)108.0=104W/m2

The ratio of 100 cars passing in afternoon to the 5 cars only passing at night is, I5carsI100cars=5100=120

Formula to calculate the expected average intensity of only 5 cars passing at night is,

I5cars=I100cars20

Substitute 104W/m2 for I100cars

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