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.

 

[rwisz]

The amplitude of a water wave can indeed change when the wave passes from deep to shallow water. This change in amplitude is due to the change in the depth of the water, which affects the speed and wavelength of the wave. In shallow water, the wave encounters more resistance and slows down, causing the wavelength to decrease and the amplitude to increase. This can be seen in some diagrams, where the amplitude is shown to increase in shallow water. However, in most books, the amplitude is assumed to remain constant for simplicity and to focus on other aspects of wave behavior. Therefore, both statements are correct and it is important to consider the context and purpose of the information being presented.