# A standing wave is set up in a string of variable length and tension by a vibrator of variable frequency. Both ends of the string are fixed. When the vibrator has a frequency f A , in a string of length L A and under tension T A , n A antinodes are set up in the string. (a) Write an expression for the frequency f A of a standing wave in terms of the number n A , length L A , tension T A , and linear density μ A . (b) If the length of the string is doubled to L B = 2 L A , what frequency f B (written as a multiple of f A ) will result in the same number of antinodes? Assume the tension and linear density are unchanged. Hint: Make a ratio of expressions for f B and f A . (c) If the frequency and length are held constant, what tension T B will produce n A + 1 antinodes? (d) If the frequency is tripled and the length of the string is halved, by what factor should the tension be changed so that twice as many antinodes are produced?

### College Physics

11th Edition
Raymond A. Serway + 1 other
Publisher: Cengage Learning
ISBN: 9781305952300

### College Physics

11th Edition
Raymond A. Serway + 1 other
Publisher: Cengage Learning
ISBN: 9781305952300

#### Solutions

Chapter
Section
Chapter 14, Problem 48P
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