Question

A fisherman notices a buoy bobbing up and down in the water in ripples produced by waves from a passing speedboat. These waves travel at $2.5 \mathrm{m} / \mathrm{s}\( and have a wavelength of \)7.5 \mathrm{m} .$ At what frequency does the buoy bob up and down?

Short answer

Answer: The buoy bobs up and down at approximately 0.333 Hz.

Step-by-step solution

Identify the given information

We are given the wave speed (v) and wavelength (λ): Wave speed (v) = 2.5 m/s Wavelength (λ) = 7.5 m

Apply the wave speed formula to solve for frequency (f)

The formula for wave speed is: v = f * λ We need to solve for frequency (f), so we'll rearrange the formula: f = v / λ

Substitute the given values into the formula

Now, we will substitute the given speed and wavelength into the formula: f = (2.5 m/s) / (7.5 m)

Calculate the frequency (f)

Divide the speed by the wavelength to find the frequency: f = 0.333... Hz

Interpret the result

The buoy bobs up and down at a frequency of approximately 0.333 Hz, or roughly once every 3 seconds.