# The minimum velocity of the length of the wave.

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 4, Problem 45RE
To determine

## To find: The minimum velocity of the length of the wave.

Expert Solution

The minimum velocity of the length of the wave is L=C

### Explanation of Solution

Given information:

The velocity of a wave of length L in deep water is V=k1C+CL

Calculation:

Consider the velocity of a wave,

V=k1C+CL=kL2+CCL

Where k and C are the positive constants,

Then derivation of V with respect to L,

V=k(L2C2)2CL2L2+C2CL

Length L is a positive quantity so L2+CCL0,[c>0]

And V=0 when L2C2=0 or L=C

So V has an absolute minimum at L=C

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