Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 11 - Oscillations and Waves - Problems - Page 324: 51

Answer

60Hz, 120Hz, 180Hz.

Work Step by Step

The frequencies of the harmonics for a string that is fixed at both ends are given by equation 11-19b. $$f_n=nf_1$$ “Four loops” is the standing wave pattern for the fourth harmonic, $240Hz=f_4=4f_1$. Therefore, other resonant frequencies include $f_1=60Hz$, aka the fundamental or the first harmonic, $f_2=2 \times 60Hz=120 Hz$, aka the first overtone or the second harmonic, and $f_3=3 \times 60Hz=180 Hz$, aka the second overtone or the third harmonic.
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