Question

On a workday the average decibel level of a busy street is 69 db, with 139 cars passing a given point every minute. if the number of cars is reduced to 17 cars every minute on a weekend, what is the decibel level of the street? answer in units of db.

Answer 1

The decibel level of the street when the number of cars is reduced to 17 per minute is approximately 57.89 dB.

Step-by-step explanation:

To find the decibel level of the street when the number of cars is reduced to 17 cars per minute, we need to understand the relationship between decibels and intensity. Decibels (dB) measure the intensity of sound, and the formula for finding the decibel level is:

dB = 10 * log(I/I0)

Where dB is the decibel level, I is the intensity of the sound, and I0 is the threshold intensity.

Since the number of cars is reducing from 139 to 17, the sound intensity will reduce proportionally.

1. First, find the intensity of the busy street (139 cars per minute) using the given decibel level of 69 dB.
2. Next, use this intensity to calculate the new decibel level when the number of cars is reduced to 17 per minute.

Let's solve the problem step-by-step:

Step 1:

To find the intensity of the busy street, we can rearrange the formula and solve for I:

I = I0 * 10(dB/10)

Given: dB = 69 dB, I0 = threshold intensity = 10⁻¹² W/m²

Substitute the values into the formula and solve for I:

I = (10⁻¹² W/m²) * 10(69/10)

I ≈ 3.162 * 10⁻² W/m²

Step 2:

To find the decibel level when the number of cars is reduced to 17 per minute, we can again use the formula:

dB = 10 * log(I/I0)

Given: I = (3.162 * 10⁻² W/m²) * (17/139)

Substitute the values into the formula and solve for dB:

dB = 10 * log(((3.162 * 10⁻² W/m²) * (17/139))/(10⁻¹² W/m²))

dB ≈ 57.89 dB

Therefore, when the number of cars is reduced to 17 per minute, the decibel level of the street is approximately 57.89 dB.

Answer 2

Decibel is directly proportional to number of cars passing the point. That is,

69 db ----- 139 cars
x db ----- 17 cars

x = number of cars passing the point per minute on a weekend.

Then,
x= (69*17)/139 = 8.43 db ≈ 8 db