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