# Waveledngth vs frequency

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

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:
$$v = \sqrt{\frac{g\lambda}{2\pi}\,tanh(2\pi\frac{d}{\lambda}})$$

which simplifies in the shallow depth limit into
$$v = \sqrt{gd}$$

so,
v=freq x wavelength

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