Velocity of a wave decreases as the water gets shallow

[kusal]

Velocity of a wave decreases as the water gets shallow. As described in-

v*v=gh
(v=velocity
g=gravity
h=depth)

as v=fλ

(λ=wave length
f=frequency)

Either f or λ has to decrease.
But as f is a constant where the same emitter is concerned the wavelength decreases.
Velocity is lower in the front of the wave than the back of it because sea gets shallow near the shore. So the wavelength decreases as it gets to the shore. But the amount of water is the same. So the amplitude has to rise. Water is pushed upwards.

What are yor comments?

 

[OlderDan]

There may be some fine points in the equations, but the basic idea is correct. Waves do travel slower in shallow water causing the back end of the wave to squeze toward the front and raise the amplitude. The slowing of the front is what causes the familiar "breaking" of ordinary waves at the shoreline.

The slowing of waves at shallower depth is the basis for "ripple tank" demonstrations of wave phenonomna.