Can someone clarify Wave Power?

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The discussion centers on the discrepancies in wave power equations, specifically the constants used in different formulas. The user references Wikipedia's formula yielding 64π, while other sources provide 8π and 32π for sinusoidal waves. The primary equation discussed is P=FwkA² sin(kx-wt)², with a focus on deriving a consistent formula based on gravity, amplitude, and period. The user emphasizes that the wave height (H) is twice the wave amplitude (a), which is crucial for accurate calculations.

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Alright, so wikipedia says:

4ceaceaf3d65c114c57a3f271b723c11.png


Where does this 64pi come from (i'm skeptical) apon further investigation I found.
http://www.esru.strath.ac.uk/EandE/Web_sites/01-02/RE_info/wave%20power.htm
Saying its 8pi

and finally

http://www.ocsenergy.anl.gov/documents/docs/OCS_EIS_WhitePaper_Wave.pdf
Saying its 32pi


Using my own physics books I've tried to derive the proper equation myself, but havn't had a match to either of these formulas.

P=FwkA^2 sin(kx-wt)^2

If someone can derive the equation I'm using to get one of these equations in terms of just
gravity, amplitude, and period, that would be great.
 
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The wave height (H) = twice the wave amplitude (a)

The Wiki formulae is for a trochoidal wave, the other two are for sinusoidal ones.
 

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