Physics: Principles with Applications (7th Edition)

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

Chapter 12 - Sound - General Problems - Page 357: 87

Answer

$L = 2.62~m$

Work Step by Step

We can find the frequency of the shorter pipe as: $f = \frac{v}{2L}$ $f = \frac{343~m/s}{(2)(2.40~m)}$ $f = 71.46~Hz$ Since the beat frequency is 6.0 Hz, the difference between the two frequencies must be 6.0 Hz. Since the longer pipe has a lower frequency, the frequency of the longer pipe is 65.46 Hz. We can find the length of the longer pipe as: $f = \frac{v}{2L}$ $L = \frac{v}{2f}$ $L = \frac{343~m/s}{(2)(65.46~Hz)}$ $L = 2.62~m$
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