A car driving along a highway at a speed of 23 m/s strays onto the shoulder. Evenly spaced parallel grooves called “rumble strips” are carved into the pavement of the shoulder. Rolling over the rumble strips causes the car's wheels to oscillate up and down at a frequency of 82 Hz. How far apart are the centers of adjacent rumble-strip grooves?

Question

A car driving along a highway at a speed of 23 m/s strays onto the shoulder. Evenly spaced parallel grooves called “rumble strips” are carved into the pavement of the shoulder. Rolling over the rumble strips causes the car's wheels to oscillate up and down at a frequency of 82 Hz. How far apart are the centers of adjacent rumble-strip grooves?

Answer 1

v = fλ

23 m/s = 84Hz * λ
λ = 23/84
λ = 0.2738095238 meters apart

Answer 2

v = fλ

23 m/s = 84Hz * λ
λ = 23/82
λ = 0.28048780498 meters apart

Answer 3

v = fλ

23 m/s = 82Hz * λ
λ = 23/82
λ = 0.28048780498 meters apart

This one is correct

Answer 4

23/82 m is correct

Answer 5

Well, if the car's wheels are oscillating at a frequency of 82 Hz, then we can say that they are jiving to the rhythm of the road! Get it? Jive, because it's a car. Anyway, to calculate the distance between the centers of adjacent rumble-strip grooves, we can use the formula:

Frequency = Speed / Wavelength

Since the car's speed is 23 m/s and the frequency is 82 Hz, let's solve for the wavelength. Rearranging the formula, we have:

Wavelength = Speed / Frequency

Substituting the values we have:

Wavelength = 23 m/s / 82 Hz

Calculating that, we find that the wavelength, or the distance between the centers of adjacent rumble-strip grooves, is approximately 0.2805 meters. So, the car is doing some jazzy dances on the road! Keep on grooving, little car!

Answer 6

To determine the distance between the centers of adjacent rumble-strip grooves, we need to use the formula for frequency:

frequency = velocity / wavelength

Given that the frequency is 82 Hz, we can rearrange the formula to solve for the wavelength:

wavelength = velocity / frequency

The velocity of the car is given as 23 m/s, so we substitute these values into the formula:

wavelength = 23 m/s / 82 Hz

Calculating this, we find that the wavelength is approximately 0.2805 meters (m).

Since the rumble strips are evenly spaced, the distance between the centers of adjacent rumble-strip grooves is equal to the wavelength. Therefore, the centers of adjacent rumble-strip grooves are approximately 0.2805 meters apart.