Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson
ISBN 10: 0321740904
ISBN 13: 978-0-32174-090-8

Chapter 21 - Superposition - Exercises and Problems - Page 623: 49

Answer

$579\;\rm Hz$, $4929\;\rm Hz$

Work Step by Step

Using the open-closed tube model, we know that the frequency is given by $$f_m=\dfrac{mv}{4L}\tag{$m=1,3,5,..$}$$ The only thing that changes here is the speed of sound waves. Hence, $$f_{m,\rm new}=\dfrac{mv_{\rm new}}{4L}$$ where, from the first formula above, $4L=mv/f_m$, so $$f_{m,\rm new}=\dfrac{v_{\rm new}}{v}f_m$$ For the first one, $$f_{m,\rm new}=\dfrac{750}{350}\cdot270=\color{red}{\bf 579}\;\rm Hz$$ For the second one, $$f_{m,\rm new}=\dfrac{750}{350}\cdot 2300=\color{red}{\bf 4929}\;\rm Hz$$
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