Question

If a water wave with length moves with velocity in a body of water with depth d , then v=Sqrt((gL/2pi)[tanh(2pid/L)])
where g is the acceleration due to gravity.
Explain why the approximation
v is approximately sqrt(gL/2pi)
is appropriate in deep water.

Answer 1

\[v=\sqrt{(gL/2\pi)(\tanh(2\pi(d)/L)}\]

Answer 2

\[\sqrt{(gL)/2\pi)}\]