Water waves

[Amber]

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

[GAHD]

Ok, From what I gater with water, In an ideal world the formula for wave height and propogation looks something like:

 

velocity = squareroot of [ (gravity * wavelength ) / ( 2 * pi )] tanh [ 2 * pi * ( depth / wavelength) ]

 

 

 

 

Stokes' Laws deal with calculating the motons of a sphere of known diameter in a fluid of known viscosity and density when subjected to an acceleration feild of known strength in an ideal world:

 

Velocity = ( 2 * Acceleration Feild Strength * radius of particle ^2 ) * ( particle density - fluid density ) / 9 * viscosity of medium

 

 

and also with knowing the force necessary to move a sphere of known diameter through a fluid of known viscosity and density at a specific speed:

 

Force = 6 * pi *Radius of the sphere * viscosity of medium * Velocity

 

Notes:

^x = an exponential value -- ex squared is ^2, cubed ^3

Acceleration = {distance/time^2} -- ex gravity is roughly 9.8m/second^2

"Ideal world" means a continuous fluid that never stops in all directions.

 

 

There are correction formulas for Stokes laws (which I don't know offhand:shrug: ) that deal with the spheres moving slower though confined spaces because the liquid has to compress against the walls of the container to allow the shere to pass.:)

 

That help?:)

[Amber]

Thank you GAHD :)

 

I think the last bit you wrote made more sense to me (words, lol)

 

I still don't understand Stoke's Law because we're not using a sphere.

[GAHD]

maby if you discribe the experiments more clearly More people will be able to relate. I only know that bit about fluid motion, though I might be able to find out.

[Amber]

Basically, I need to know why the speed of a water wave is faster with deeper water.

 

I would fill the tray with certain depths and displace the tray by the same amount each time, timing how long for 5 waves to be produced. I would then find out the speed by using v = d/t

 

My reasoning:

Considering the use of a tray, when the water waves encounter a barrier, it will slow down - so the less water there is, the more "barriers" are in contact. Therefore the more volume of water there is, the faster the speed because there is less contact so less chance of frictional forces acting upon the water. Does that sound correct?

 

I need to know about laminar flow and how this relates to the speed of the wave. Unfortunately, the textbook I have isn't very useful as it only talks about it briefly. Is there any resources on the Internet that I could read? I've tried doing a goole search, but I don't think I'm very efficient at finding information as it's just so vast on the Internet.

 

I hope it makes sense, I'm terrible at explaining things.

 

Thank you,

- Amber