Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson
ISBN 10: 0321740904
ISBN 13: 978-0-32174-090-8

Chapter 21 - Superposition - Exercises and Problems: 8

Answer

(a) There will be eight antinodes. (b) The new frequency is $2 f_0$

Work Step by Step

(a) The standing wave shows 4 antinodes, so the figure shows the fourth harmonic. If the frequency is doubled, then this will be the eight harmonic, which has eight antinodes. (b) $v \propto \sqrt{T}$ If the tension $T$ increases by a factor of four, then the speed increases by a factor of 2. We know that $f = \frac{v}{\lambda}$. If the speed doubles while the wavelength remains the same, then the frequency must also double. The new frequency is $2 f_0$.
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