Amplitude of a wave when changing depth

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When water waves transition from deep to shallow water, their wavelength and velocity decrease, while the amplitude increases. This phenomenon is often debated in literature, with some sources claiming amplitude remains constant. The increase in amplitude can be explained through the conservation of energy, where a decrease in kinetic energy (KE) corresponds to an increase in potential energy (PE). The relationship can be mathematically supported, reinforcing the concept that energy remains constant during this transition. Understanding this principle is crucial for accurately interpreting wave behavior, especially in contexts like tsunamis.
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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?
 
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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)
 
rock.freak667 said:
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?
 
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.
 

Thread 'Magnitude of buoyant force in fluids of different densities'

The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?
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