Shallow water and deep water

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Muzette

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While doing some EK 1001 problems for Physics, some of the explanations say that the surface wave velocity of a shallow water is v=squareroot(gy) and for deep water is v=squareroot(g*wavelength/2pi). In another section, it says that the velocity of water is v=squareroot(2gh). Where do these equations originate and is this something I should memorize? I don't remember running into these equations in the review books..
 
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