Waveledngth vs frequency

[labview1958]

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

 

[Fightfish]

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
$$v = \sqrt{gd}$$

 

[labview1958]

so,
v=freq x wavelength

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