# Chapter 12 - Problems - Page 465: 49

$f_r = f~\left(\frac{u+v}{u-v}\right)$

#### Work Step by Step

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: $f_r = \left(\frac{u}{u-v_s}\right)~f_o$ $f_r = \left(\frac{u}{u-v}\right)~\left(\frac{u+v}{u}\right)~f$ $f_r = f~\left(\frac{u+v}{u-v}\right)$

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