Waveledngth vs frequency

  • #1
If the frequency of a water wave is doubled in a ripple tank, is the wavelength halved? The depth of water is kept constant.

Answers and Replies

  • #2
Yes. In shallow water, the speed of the water waves is dependent only on the depth (and the gravitational acceleration g).

The general expression for the speed of a water wave is given by:
[tex]v = \sqrt{\frac{g\lambda}{2\pi}\,tanh(2\pi\frac{d}{\lambda}})[/tex]

which simplifies in the shallow depth limit into
[tex]v = \sqrt{gd}[/tex]
  • #3
v=freq x wavelength

Thus double the frequency the wavelength is halved in shallow water.