Answer
$\Delta f=136Hz$
Work Step by Step
Use equation $f'=f\Big(\frac{v_{snd}\pm v_{obs}}{v_{snd}\mp v_{source}}\Big)$, upper signs if moving toward each other and lower signs if moving away from each other.
1. Blood is observer moving away from sound source. $v_{source}=0m/s$
$f'=f\Big(\frac{v_{snd}-v_{obs}}{v_{snd}}\Big)$ for blood moving away from source
2. Blood is the sound source moving away from observer at rest $v_{obs}=0m/s$
$f''=f'\Big(\frac{v_{snd}}{v_{snd}+v_{source}}\Big)$ for blood moving away from observer
$f''=f\Big(\frac{v_{snd}- v_{obs}}{v_{snd}}\Big)\Big(\frac{v_{snd}}{v_{snd}+v_{source}}\Big)$
$f''=f\Big(\frac{v_{snd}-v_{obs}}{v_{snd}+v_{source}}\Big)$
Beat frequency $\Delta f = f''-f=f\Big(\frac{v_{snd}-v_{obs}}{v_{snd}+v_{source}}\Big)-f$
$v_{blood} = v_{obs}=v_{source}$
$\Delta f =f\Big(\frac{v_{snd}-v_{blood}}{v_{snd}+v_{blood}}\Big)-f=f\Big(\frac{2v_{blood}}{v_{snd}+v_{blood}}\Big)$
$\Delta f=(3.5\times10^6Hz)\Big(\frac{2(3\times10^{-2}m/s)}{1540m/s+3\times10^{-2}m/s}\Big)=136Hz$
