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 325: 54

Answer

The fundamental frequency is 302 Hz. The first overtone is 604 Hz. The second overtone is 906 Hz.

Work Step by Step

We can find the speed $v$ of the wave as: $v = \sqrt{\frac{F_T}{\mu}}$ $v = \sqrt{\frac{F_T}{m/L}}$ $v = \sqrt{\frac{520~N}{0.0034~kg/0.92~m}}$ $v = 375~m/s$ We can find the fundamental frequency using the formula below. Note that $L = 0.62~m$ from the bridge to the support post. $f_1 = \frac{v}{2L}$ $f_1 = \frac{375~m/s}{(2)(0.62~m)}$ $f_1 = 302~Hz$ We can find the first two overtones as: $f_2 = 2~f_1 = (2)(302~Hz) = 604~Hz$ $f_3 = 3~f_1 = (3)(302~Hz) = 906~Hz$
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