If a water wave with length L moves with velocity v across a body of water with depth d
Chapter 11, Problem 35(choose chapter or problem)
If a water wave with length L moves with velocity v across a body of water with depth d, as in the figure on page 782, then v 2 tL 2 tanh 2d L (a) If the water is deep, show that v < stLys2d. (b) If the water is shallow, use the Maclaurin series for tanh to show that v < std . (Thus in shallow water the velocity of a wave tends to be independent of the length ofthe wave.)(c) Use the Alternating Series Estimation Theorem to showthat if L . 10d, then the estimate v 2 < td is accurate towithin 0.014tL.
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