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 621: 15

Answer

$512\;\rm Hz$

Work Step by Step

We know, in the open-open tube, that the frequency is given by $$f_m=\dfrac{mv}{2L}$$ and for the fundamental frequency, $$f_1=\dfrac{ v}{2L}$$ For the helium case, $$f_1=\dfrac{ v_{He}}{2L}$$ Hence, $$2L=\dfrac{ v_{He}}{f_1}\tag 1$$ in the air case, $$f_2=\dfrac{ v_{air}}{2L}$$ Plugging $2L$ from (1); $$f_2=\dfrac{ v_{air}f_1}{v_{He}}$$ Plugging the known; $$f_2=\dfrac{ (331)(1500)}{(970)}$$ $$f_2=\color{red}{\bf512}\;\rm Hz$$
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