EK physics #656, page 68

[lilmc]

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Hi! Can anyone explain #656 in the EK physics 1001 book? It acts for the velocity of a wave that is propagating through water. A ball rests on the wave an oscillates with an amplitude of y every t seconds. The depth of the water is h.
I tried to find the velocity using conservation of energy. I thought that if I found the maximum y direction of the velocity of the ball this would give me the right answer. It did not. The answer is sqrt(gh), can anyone explain this answer?

Thanks in advance!

 

[K1N6]

Hello there, I admit after I saw this post I took a stab at the problem myself and got it incorrect as I chose the acceleration due to gravity times the wavelength.
I know that the amplitude of the wave 👍 has nothing to do with speed of the wave itself (v=lamba*frequency) but I was caught off guard by the shallow water equation which I've never seen before or If I did I deemed it as something that would appear in the passage.

In shallow water, the wave velocity is proportional to depth
In deep water, the wave velocity is proportional to wavelength.

http://hyperphysics.phy-astr.gsu.edu/hbase/watwav.html

Don't get hung up on this stuff, that's what I did and I missed my opportunities to really hit my weaknesses.

 

[lilmc]

thanks, that's a good point that it might end up being in the passage. Thanks for the help and advice!!