Fundamentals of Physics Extended (10th Edition)

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

Chapter 17 - Waves-II - Questions - Page 505: 10

Answer

The sound produced by the string will cause resonance in pipe d, and the resonance will be the fundamental frequency $n=1$

Work Step by Step

We can find an expression for the fundamental frequency of the string: $f = \frac{v}{\lambda} = \frac{v}{2L} = 0.5~\frac{v}{L}$ We can find an expression for the resonant frequencies of pipe a: $f = \frac{nv}{4L},$ where $n = 1,3,5,...$ $f = 0.25~\frac{v}{L}, 0.75~\frac{v}{L}, 1.25~\frac{v}{L},...$ We can find an expression for the resonant frequencies of pipe b: $f = \frac{nv}{4(2L)},$ where $n = 1,3,5,...$ $f = 0.125~\frac{v}{L}, 0.375~\frac{v}{L}, 0.625~\frac{v}{L},...$ We can find an expression for the resonant frequencies of pipe c: $f = \frac{nv}{2(L/2)},$ where $n = 1,2,3,...$ $f = \frac{v}{L}, 2~\frac{v}{L}, 3~\frac{v}{L},...$ We can find an expression for the resonant frequencies of pipe d: $f = \frac{nv}{4(L/2)},$ where $n = 1,3,5,...$ $f = 0.5~\frac{v}{L}, 1.5~\frac{v}{L}, 2.5~\frac{v}{L},...$ The sound produced by the string will cause resonance in pipe d, and the resonance will be the fundamental frequency $n=1$
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