Homework Help: Calculating the wavelength of a surface wave after impact

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1. Dec 8, 2018 at 7:06 AM

LordOfCinders

1. The problem statement, all variables and given/known data
There's a bucket, filled about halfway with water. The water itself is completely still. A perfect sphere with mass m and volume v are given. The depth of the water, and the radius of the bucket (which may be considered perfectly cylindrical) are both given. In short, you know everything.

Calculate the wavelength of a surface wave after impact of the sphere with the surface water.

2. Relevant equations
My issue with this question is that I still have no idea what formulas I actually have to use. However, there are a few things I assumed:

Ekin = (1.2)*m*v^2
Fz = m * g (g being 9.81 [m/s^2])
W = F * S
v = root(g * h)
c = root((g * wavelength)/(2pi))

3. The attempt at a solution

As stated before, I am clueless. The only reason I even believe the kinetic energy and gravity are important, is because I suppose that there's either a transfer of forces, or a transfer of energy. I do not need to be fed the answer to this question, but it would help me greatly if someone knew of a formula that I myself could not find (after about an hour of searching using terms such as "surface wave after impact")

2. Dec 13, 2018 at 6:00 PM

PF_Help_Bot

Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.

3. Dec 13, 2018 at 6:11 PM

scottdave

Unless the mass or volume of the sphere are significant, compared to the dimensions (and mass) of the water bucket, I think the wavelength is going to depend on the features of the bucket/water almost exclusively. The ball simply disturbs the water and starts the wave. After that, it has not much effect.

There would be different modes that the standing wave could operate in.