## College Physics (4th Edition)

Published by McGraw-Hill Education

# Chapter 12 - Problems - Page 463: 27

#### Answer

The longest possible length of the tube is $8.575~mm$

#### Work Step by Step

The wavelength of the fundamental frequency of a pipe that is open at both ends is $\lambda = 2L$. We can let $v = 343~m/s$ be the speed of sound in air. We can find the maximum length of the tube: $\lambda = \frac{v}{f}$ $2L = \frac{v}{f}$ $L = \frac{v}{2f}$ $L = \frac{343~m/s}{(2)(20,000~Hz)}$ $L = 0.008575~m$ $L = 8.575~mm$ The longest possible length of the tube is $8.575~mm$

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