   Chapter 14, Problem 77AP

Chapter
Section
Textbook Problem

On a workday, the average decibel level of a busy street is 70.0 dB, with 100 cars passing a given point every minute. If the number of cars is reduced to 25 every minute on a weekend, what is the decibel level of the street?

To determine
The decibel level of the street.

Explanation

Given Info: The average decibel level of a busy street is 70.0 dB

Formula to calculate the average decibel level of a busy street is,

β1=10log(I100carsI0)

• β1 is the decibel level.
• I100cars is the intensity of the 100 cars passing over a given point.
• I0 is the reference intensity.

Substitute 70.0 dB for β1 and 1012W/m2 for I0 to find I100cars .

70.0dB=10log(I100cars1012W/m2)I100cars=105W/m2 (1)

Formula to calculate the intensity of the 75 cars passing over a given point

I75cars=0.75(105W/m2) (2)

• I75cars is the intensity of the 75 cars passing over every minute.

Rewrite the equation (2) we get,

I75cars=7.5×106W/m2 (3)

Thus, the intensity of the 75 cars passing over a given point in every minute is 7

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