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:

$v=\frac{\mathrm{\Delta }S}{\mathrm{\Delta }t}=\frac{12\mathrm{m}}{4.0\mathrm{s}}=3.0\mathrm{m}/\mathrm{s}$.

We are given information about wavelength, so we can solve the problem using the following relationship between velocity, wavelength, and frequency:

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