# Waveledngth vs frequency

1. Mar 29, 2010

### 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.

2. Mar 29, 2010

### 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
$$v = \sqrt{gd}$$

3. Mar 30, 2010

### labview1958

so,
v=freq x wavelength

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