To determine The length of the wave that results in the minimum velocity. If, In deep water, the velocity of a wave is v = k ( l a + a l ) , where a and k are constants, and l is the length of the wave. Explanation Step :1 The velocity v of a wave is, v = k ( l a + a l ) . Note that, a and k are positive constants and l is the length of the wave. Step 2: Differentiate v with respect to l . v = k ( l a + a l ) d v d l = k ( 1 a − a l 2 2 ( l a + a l ) ) = k ( − a l 2 + 1 a 2 ( l a + a l ) ) Step 3: For maxima and minima d v d l = 0 Hence, k ( a l 2 − 1 a 2 ( l a + a l ) ) = 0 a l 2 − 1 a = 0 a l 2 = 1 a l 2 = a 2 Simplify further as follows. l 2 = a 2 l = a Differentiate d v d l with respect to l . d v d l = k 2 ( − a l 2 + 1 a ( l a + a l ) ) d 2 v d l 2 = k 2 ( ( 2 ) a l 3 ( ( l a + a l ) ) + ( − a l 2 + 1 a ) ( 1 2 ) ( − a l 2 + 1 a ( l a + a l ) ) ( ( l a + a l <

Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

11th Edition

ISBN: 9780137554843

Author: Allyn Washington, Richard Evans

Publisher: PEARSON+

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Chapter 24.7, Problem 13E

To determine

The length of the wave that results in the minimum velocity. If, In deep water, the velocity of a wave is v=k(la+al), where a and k are constants, and l is the length of the wave.

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Chapter 24.7, Problem 12E

Chapter 24.7, Problem 14E

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Chapter 24 Solutions

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