College Physics (4th Edition)

Published by McGraw-Hill Education
ISBN 10: 0073512141
ISBN 13: 978-0-07351-214-3

Chapter 12 - Problems - Page 465: 57


The beat frequency is $637~Hz$

Work Step by Step

Let $u$ be the speed of sound in the blood and let $v$ be the speed of the blood flow. To find the frequency received by the moving blood, we can use the equation for the Doppler effect when the observer is approaching: $f_o = \left(\frac{u+v_o}{u}\right)~f$ $f_o = \left(\frac{u+v}{u}\right)~f$ To find the reflected frequency, we can let $f_o$ be the sound source and use the equation for the Doppler effect when the source is approaching: $f_r = \left(\frac{u}{u-v_s}\right)~f_o$ $f_r = \left(\frac{u}{u-v}\right)~\left(\frac{u+v}{u}\right)~f$ $f_r = f~\left(\frac{u+v}{u-v}\right)$ $f_r = (5.0~\times 10^6~Hz)~\left(\frac{1570~m/s+0.10~m/s}{1570~m/s-0.10~m/s}\right)$ $f_r = 5,000,637~Hz$ The beat frequency is the difference between the emitted frequency and the reflected frequency. We can find the frequency difference: $5,000,637~Hz - 5,000,000~Hz = 637~Hz$ The beat frequency is $637~Hz$
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