Physics Exercises/Vibrations and Sound

Waves, basic
The distance between successive crests in the waves in the ocean is 7.5 m. The crests travel 12 m in 4.0 s.  What is the frequency of a buoy bobbing up and down in this water?

Solution
First, we calculate the velocity of water wave: $$v = \frac{\Delta S}{\Delta t} = \frac{12~\mathrm{m}}{4.0~\mathrm{s}} = 3.0~\mathrm{m/s}$$. We are given information about wavelength, so we can solve the problem using the following relationship between velocity, wavelength, and frequency: $$f = \frac{v}{\lambda} = \frac{3.0~\mathrm{m/s}}{7.5~\mathrm{m}} = 0.40~\mathrm{Hz}$$.