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 625: 73

Answer

$7\;\rm m/s$

Work Step by Step

The number of beats per second in this case is given by $$ f_-=400-8=\bf 392\;\rm Hz$$ where $f_+$ is the frequency of the speaker on the ground and $f_-$ is the frequency of the speaker on the truck. We also know that $$f_-=\dfrac{v}{v+v_{car}}f$$ where $v_{}$ is the speed of sound wave. $$v+v_{car} =v\dfrac{f}{f_-}$$ $$ v_{car} =v\dfrac{f}{f_-}-v$$ $$ v_{car} =v\left[\dfrac{f}{f_-}-1\right]$$ Plugging the known; $$ v_{car} =343\left[\dfrac{400}{392}-1\right]$$ $$ v_{car} =\color{red}{\bf 7}\;\rm m/s$$
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