Why is Frequency maintained, and is the answer true for both types of wave

alexjdyer

I ask this question in relation to how frequency is preserved during refraction and also to ask if the preservation of frequency causes the increase in amplitude of a tsunami when it approaches the shore.

I am aware that:
λf=v
v^2 = g h in shallow water where v is wavespeed, and h is the height of the wave.
_1μ_2=v1/v2 the refractive index and the velocity in mediums 1 and 2


I assume that when a tsunami reaches the shore it is slowed down. For frequency to be preserved, wavelength must decrease. However if the "width" of the wave is decreased but the volume remains the same then the height, or amplitude must increase. This is why i think frequency is linked to tsunamis, but i do not understand why.

Any help would be vastly appreciated