Amplitude of a wave when changing depth

[nilic1]

In most books the amplitude does not change when water waves pass from deep to shallow water. In some books the diagrams show an increased amplitude. Which one is correct?

 

[rock.freak667]

As a wave goes from deep to shallow, its wavelength decreases as well as its velocity. As it approaches a shallow part, the amplitude increases.

(an easy example is to consider how a tsunami works)

 

[nilic1]

As a wave goes from deep to shallow, its wavelength decreases as well as its velocity. As it approaches a shallow part, the amplitude increases.

(an easy example is to consider how a tsunami works)

Thanks for your answer. Is there any mathematical relationship which can support the fact that the amplitude actually increases?

 

[rock.freak667]

I can't remember what power of a wave depends on how however, if you consider a conservation of energy standpoint, I think if the second velocity decreases (decrease in KE) the height would increase (increase in PE) to keep the energy constant.

KE + PE = constant.