Solved: If a water wave with length moves with velocity

Chapter 8, Problem 8.8.26

(choose chapter or problem)

If a water wave with length moves with velocity across a body of water with depth , as in the figure, then (a) If the water is deep, show that . (b) If the water is shallow, use the Maclaurin series for to show that . (Thus in shallow water the velocity of a wave tends to be independent of the length of the wave.) (c) Use the Alternating Series Estimation Theorem to show that if , then the estimate is accurate to within .

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