College Physics (4th Edition)

Published by McGraw-Hill Education
ISBN 10: 0073512141
ISBN 13: 978-0-07351-214-3

Chapter 12 - Problems - Page 464: 33


The temperature inside the pipe is $41.7^{\circ}C$

Work Step by Step

To find the correct harmonic, we can let the speed of sound in air be $343~m/s$: $\lambda_n = \frac{v}{f_n}$ $\frac{2L}{n} = \frac{v}{f_n}$ $n = \frac{2L~f_n}{v}$ $n = \frac{(2)(2.0~m)(702~Hz)}{343~m/s}$ $n = 8.2$ Since this value is close to $8$, we can assume that the experiment uses the 8th harmonic. We can find the speed of sound inside the pipe: $v = \lambda_8~f_8$ $v = \frac{2L}{8}~f_8$ $v = \frac{(2)(2.0~m)}{8}~(702~Hz)$ $v = 356~m/s$ We can find the temperature inside the pipe: $331+0.6~T = 356$ $T = \frac{356-331}{0.6}$ $T = 41.7^{\circ}C$ The temperature inside the pipe is $41.7^{\circ}C$
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