## Why do waves have a shorter wavelength in shallower water?

Question

Here’s my very limited and vague answer that really bears not too much detail:

The Wave fronts are closer together and since the frequency is constant, and v = f*lambda, if lambda has decreased therefore v has too.

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General Physics
4 years
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## Answer ( 1 )

Your answer is wrong. water waves on the surface are on the plane with the depth. They are in the form z = a sin(kx +my-wt)

If y is the direction of the depth then m is inversely proportional to the depth. Along x axis it will have the wave length proportional to

w/k = sqrt( v^2 – (w/l)^2). you see that wave length can be kilo meter length in the horizontal direction. Idea is similar to wave guides. These waves are controlled by the gravity. Therefore, they are called as the gravity waves. Here v is the velocity of the waves.