Question

Special sections of roadway are sometimes paved with "rumble strips" to alert inattentive drivers. In a particular case the grooves are spaced L = 0.25 m apart and the depth of each groove is d= 0.45 cm. As you drive over this rumble strip, the tires of your car oscillate about their equilibrium positions with a frequency off = 67 Hz. Refer to the figure, which is not drawn to scale.

Answer 1

The frequency of the vibrations of the tire is 750 Hz when the car moves at 30.0 m/s, with crevices spaced 2.00 cm apart.

Step-by-step explanation:

To find the frequency of the vibrations of the tire, we need to determine the wavelength of each crevice. The crevices are spaced 2.00 cm apart, so we can calculate the wavelength using the formula:

λ = 2 * distance between crevices

Plugging in the value for the distance between crevices (2.00 cm = 0.02 m) gives us:

λ = 2 * 0.02 m = 0.04 m

The frequency (f) of the vibrating tire can be calculated using the formula:

f = v / λ

Plugging in the given value for the speed of the car (30.0 m/s) and the calculated value for the wavelength (0.04 m) gives us:

f = 30.0 m/s / 0.04 m = 750 Hz

Therefore, the frequency of these vibrations is 750 Hz.