Fundamentals of Physics Extended (10th Edition)

Published by Wiley
ISBN 10: 1-11823-072-8
ISBN 13: 978-1-11823-072-5

Chapter 16 - Waves-I - Problems - Page 475: 48a

Answer

$$ 6.36 \mathrm{Hz} $$

Work Step by Step

Using Eq. $16-26$ , we find the wave speed to be $$ v=\sqrt{\frac{\tau}{\mu}}=\sqrt{\frac{65.2 \times 10^{6} \mathrm{N}}{3.35 \mathrm{kg} / \mathrm{m}}}=4412 \mathrm{m} / \mathrm{s} $$ Corresponding resonant frequencies will be $$ f_{n}=\frac{n v}{2 L}=\frac{n}{2 L} \sqrt{\frac{\tau}{\mu}}, \quad n=1,2,3, \ldots $$ lowest (fundamental) resonant frequency $f_{1}$ is $\lambda_{1}=2 L,$ where $L=347 \mathrm{m}$ . Thus, $$ f_{1}=\frac{v}{\lambda_{1}}=\frac{4412 \mathrm{m} / \mathrm{s}}{2(347 \mathrm{m})}=6.36 \mathrm{Hz} $$
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