College Physics (4th Edition)

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

Chapter 12 - Problems - Page 466: 66


The four lowest standing wave frequencies are: $f_1 = 17.9~Hz$ $f_3 = 53.7~Hz$ $f_5 = 89.5~Hz$ $f_7 = 125.3~Hz$

Work Step by Step

We can find the fundamental frequency: $f = \frac{v}{\lambda}$ $f = \frac{v}{4L}$ $f = \frac{343~m/s}{(4)(4.80~m)}$ $f = 17.9~Hz$ In a pipe that is closed at one end, the standing wave frequencies have the form $~f, ~3f, ~5f, ~7f, ~9f, ~etc...$ We can find the four lowest standing wave frequencies: $f_1 = 17.9~Hz$ $f_3 = (3)(17.9~Hz) = 53.7~Hz$ $f_5 = (5)(17.9~Hz) = 89.5~Hz$ $f_7 = (7)(17.9~Hz) = 125.3~Hz$
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