Investigating Wave Speed in Water: Uncovering the Theory

AI Thread Summary
Wave speed in water increases with depth due to reduced interaction with the bottom surface, which minimizes friction and energy loss. This phenomenon is influenced by Stoke's Law, where viscosity plays a role in wave propagation. In shallower water, waves encounter more barriers, leading to slower speeds as energy is dissipated. The concept of laminar flow is relevant, as it describes how water moves in layers, affecting wave behavior. Understanding these principles can clarify the relationship between water depth and wave speed.
Amber
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I'm doing an investigation on how the speed of a wave varies as the depth of water changes, using a tray of water. I know that in deeper water the speed will be quicker than that in shallow water. However I don't quite understand why this is. Apparently it has something to do with Stoke's Law? Is it related to the viscosity and the flow of water in different conditions - the more volume there is, the faster it will travel? Please help me with the theory behind it to help me understand better.

Thank you,
- Amber
 
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Try to think of the problem along this line, a ball is traveling along a frictionless surface at a constant speed, but when it start traveling uphill, its speed decreases because the kinetic energy of the ball is being converted into gravitational potential energy.

So, what would happen to a water wave when it encounters a barrier?
 
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Thank you.

When the water waves encounter a barrier, it will slow down - so the less water there is, the more "barriers" are in contact. Therefore in shallower water the speed is slower? Is that correct?

It would help if the teacher taught us properly instead of asking us to read the textbook, and I find that doesn't help much.

Now I need to know how laminar flow relates to all this :confused:
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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