An interstate highway has been built though a poor neighborhood in a city. In the afternoon, the sound level in a rented room is 114.0 dB as 172 cars pass outside the window every minute. Late at night, the traffic flow is only 7 cars per minute.

Question

An interstate highway has been built though a poor neighborhood in a city. In the afternoon, the sound level in a rented room is 114.0 dB as 172 cars pass outside the window every minute. Late at night, the traffic flow is only 7 cars per minute.

(b) What is the sound intensity at night? (c) What is the average late-night sound level?

Answer 1

86 cars (half of them) is 3 db down

43 cars will be down another 3 db
22 cars (appx) will be down another 3 db
11 cars will be down another 3 db

I estimating, 7 cars will be 114-14 db.

Doing the math:
Intnsity=10log(power/E-12)
112=10log(EachCar*172/E-12)
11.2=log( )
taking theantilog of each side.

E11.2=Each car*172/E-12
E-.8=each car*172

each car= .158/172

sound intensity at night:
Inight=10log(7*.158/172E-12)=98db

Answer 2

To find the answers to these questions, we need to understand the relationship between sound level, sound intensity, and the number of cars passing by.

Sound level, measured in decibels (dB), is a logarithmic scale that represents the intensity of sound waves. Sound intensity, measured in watts per square meter (W/m²), is the actual physical measure of the sound energy passing through a particular area.

The relationship between sound level and sound intensity is given by the equation:

Sound Level (dB) = 10 * log10(Sound Intensity (W/m²) / Reference Intensity)

The reference intensity is the threshold of hearing, which is usually taken to be 1 * 10^-12 W/m².

Now let's find the answers to the questions:

(b) What is the sound intensity at night when traffic flow is 7 cars per minute?

To calculate the sound intensity, we need to know the sound level and the reference intensity.

Given:
Sound Level during the afternoon = 114.0 dB
Traffic flow at night = 7 cars per minute

First, we need to convert the traffic flow rate into a unit that relates to sound intensity. One way to do this is to convert cars per minute to cars per second:

Traffic flow at night = 7 cars per minute = 7/60 cars per second

Next, we need to determine the sound intensity at night using the given sound level and the reference intensity. Rearranging the sound level equation, we can express the sound intensity in terms of the reference intensity:

Sound Intensity (W/m²) = 10^(Sound Level (dB) / 10) * Reference Intensity

Substituting the given values:
Sound Intensity (W/m²) = 10^(114.0 / 10) * 1 * 10^-12

Calculating the result:
Sound Intensity (W/m²) = 3.98107 * 10^-1 W/m²

Therefore, the sound intensity at night when traffic flow is 7 cars per minute is approximately 3.98107 * 10^-1 W/m².

(c) What is the average late-night sound level?

To calculate the average late-night sound level, we need to find the number of cars passing per minute and use that information to determine the sound level.

Given:
Traffic flow at night = 7 cars per minute

To calculate the average sound level, we need to know the sound intensity and the reference intensity. Using the formula mentioned earlier:

Sound Level (dB) = 10 * log10(Sound Intensity (W/m²) / Reference Intensity)

Plugging in the values:
Sound Level (dB) = 10 * log10((3.98107 * 10^-1) / (1 * 10^-12))

Calculating the result:
Sound Level (dB) = 10 * log10(3.98107 * 10^11)

Sound Level (dB) ≈ 107.98 dB

Therefore, the average late-night sound level is approximately 107.98 dB.