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

 

[jbsteele]

. The answer to your question lies in the conservation of energy. When a tsunami approaches the shore, the water depth decreases and the wave speed decreases, meaning the wavelength gets shorter. This decrease in wavelength is accompanied by an increase in wave height, or amplitude, to conserve the energy of the wave. This is because as the wavelength decreases, the frequency remains the same but the energy density increases. The energy that was previously spread out over a longer wavelength must be concentrated into a shorter wavelength, thus increasing the wave height.