Final answer:
The frequency of the vibrations of the tire's tread pattern, when the car is moving at 30.0 m/s, is 1500 Hertz (Hz). This is calculated by dividing the speed of the car by the distance between the crevices on the tire, after converting the crevice distance to meters.
Step-by-step explanation:
To determine the frequency of the vibrations made by the tire's tread pattern, we can use the relationship between frequency (f), speed (v), and the distance between the crevices (d). Since each crevice in the tread pattern generates a single vibration as the tire moves over it, the frequency can be calculated by dividing the speed of the car by the distance between crevices.
The formula for frequency in this context is: f = v / d.
Given that the car is moving at a speed of 30.0 meters per second (m/s) and the distance between the crevices on the tire is 2.00 centimeters (cm), we must first convert the distance from centimeters to meters to match the units of speed. There are 100 centimeters in a meter, so the distance is 0.02 meters (2.00 cm).
Now, applying the formula:
f = 30.0 m/s / 0.02 m
f = 1500 s⁻¹
The frequency of the vibrations is 1500 vibrations per second, also known as 1500 Hertz (Hz).