Question

Tapping the surface of a pan of water generates 17.5 waves per second. If the wavelength of each wave is 45 cm, what is the speed of the waves?1) 7.9 m/s2) 790 m/s3) 39 m/s4) 2.6 m/s

Answer 1

The frequency of the waves is 17.5 Hz, and their wavelength is 45cm. Recall the following reation between the frequency, the wavelength and the speed of a wave:

$v=\lambda f$

Substitute f=17.5Hz and λ=45cm to find the speed of the wave:

$\begin{gathered} v=(45\operatorname{cm})(17.5Hz) \\ =787.5\frac{\operatorname{cm}}{s} \\ =7.875\frac{m}{s} \\ \approx7.9\frac{m}{s} \end{gathered}$

Therefore, the speed of the waves is:

$7.9\frac{m}{s}$