# Water Wave

1. Aug 18, 2004

### no idea

why water wave travel more slowly in shallow water than deep water?

2. Aug 18, 2004

### ArmoSkater87

Probably because of friction against the shallow ground.

3. Aug 19, 2004

Its probably because of the difraction of the wave. Off land, in deep water, the wave is more compact and has a higher amplitude. But once the wave gets to shalower water and moves inland, it diffracts, spreads out, and loses amplitude. This causes it to lose energy, and speed. It also could be because of friction.

4. Aug 20, 2004

### no idea

What is the relationship between speed and amplitude?Is the formula Speed=wave length*frequency?

5. Aug 20, 2004

### arildno

First of all, why does a given wave travel faster in deep water ?
To answer this sufficiently, we may regard the linear dispersion relation, which relates the wavenumber "k" with the phase velocity "c":
$$c=\sqrt{\frac{g}{k}}\sqrt{Tanh(kh)}$$
g is the acceleration of gravity, whereas "h" is the water depth.
Keeping the wavelength (and hence, k) constant and varying "h" we see that "c" increases with "h", having as maximum $$\sqrt{\frac{g}{k}}$$

Secondly, how does the phase velocity vary with the wave amplitude?
(This is called "amplitude dispersion")
This is a (stongly) non-linear effect, suffice it to say that the phase velocity increases with the amplitude.