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: 86

Answer

(a) The beat frequency is zero. (b) (a) The beat frequency is 24.4 Hz (c) The beat frequency is zero.

Work Step by Step

(a) Since both speakers are approaching at the same speed, the frequency heard by the stationary observer is the same from both speakers. Since there is no difference in frequencies, the beat frequency is zero. (b) We can find the frequency $f_a$ heard from the approaching speaker. $f_a = \frac{f}{(1-\frac{v_{source}}{v_{snd}})}$ $f_a = \frac{348~Hz}{(1-\frac{12.0~m/s}{343~m/s}~)}$ $f_a = 360.6~Hz$ We can find the frequency $f_r$ heard from the receding speaker. $f_r = \frac{f}{(1+\frac{v_{source}}{v_{snd}})}$ $f_r = \frac{348~Hz}{(1+\frac{12.0~m/s}{343~m/s}~)}$ $f_r = 336.2~Hz$ The beat frequency is the difference between the two frequencies $360.6~Hz$ and $336.2~Hz$. Therefore, the beat frequency is $24.4~Hz$ (c) Since both speakers are receding at the same speed, the frequency heard by the stationary observer is the same from both speakers. Since there is no difference in frequencies, the beat frequency is zero.
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