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# If a water wave with length $L$ moves with velocity $v$ in a body of water with depth $d,$ then$v = \sqrt {\frac {gL}{2 \pi} \tanh (\frac {2 \pi d}{L}}$where $g$ is the acceleration due to gravity. (See Figure 5.) Explain why the approximation$v \approx \sqrt {\frac {gL}{2 \pi}}$ is appropriate in deep water.

## $\sqrt{\frac{g L}{2 \pi}}$

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### Video Transcript

Okay, we know that tan of two pi d over l We know we can write this as the limit as D approaches positive infinity of each of the four Pi di over Al to the minus one. This simplifies to the square root of G l over to pie. Now remember, that is the duct increases the function 10 h of two pied de over Al goes towards one though for the velocity as she out over too pie.

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