How Does Water Depth Affect Wave Speed and Particle Motion?

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Yuqing
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I have trouble understanding why water waves tend to speed up for waters deeper than 1/2 wavelength and slow down for waters shallower. I have read it has something to do with how the particle orbit changes to elliptical in shallow waters.

Why does the particle orbit become a flat ellipse in shallow water and is that the factor influencing the slower wave speed? If not not, what is?
 
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