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: 80

Answer

4 Hz.

Work Step by Step

Use the equation for the fundamental frequency of a tube closed at one end. $$f=\frac{v}{4L}$$ In the hot tube, the speed of sound increases, so we have two different frequencies. $$\frac{f_{31}}{f_{25}}=\frac{v_{31}}{v_{25}}$$ $$ f_{31} = f_{25}\frac{v_{31}}{v_{25}}$$ The beat frequency is the difference in frequencies. $$\Delta f=f_{31}-f_{25}=f_{25}\left(\frac{v_{31}}{v_{25}}-1 \right)$$ $$\Delta f=(349Hz)\left(\frac{331+0.60(31.0)}{331+0.60(25.0)}-1 \right)=3.63Hz\approx4Hz$$
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