Answer
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 $637~Hz$
