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:

$f={\frac {v}{\lambda }}={\frac {3.0~\mathrm {m/s} }{7.5~\mathrm {m} }}=0.40~\mathrm {Hz}$.