Solution: If a water wave with length moves with velocity across a body of water with
Chapter 11, Problem 35(choose chapter or problem)
If a water wave with length moves with velocity across a body of water with depth , as in the figure on page 776, 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 thewave.)(c) Use the Alternating Series Estimation Theorem to show thatif , then the estimate is accurate to within.
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