Blood flow rates can be found by measuring the Doppler shift infrequency of ultr

Question

Blood flow rates can be found by measuring the Doppler shift infrequency of ultrasound reflected by red blood cells (known asangiodynography). If the speed of the red blood cells is v, thespeed of sound in blood is u, the ultrasound source emits waves offrequency f, and we assume that the blood cells are moving directlytoward the ultrasound source, show that the frequency fr, ofreflected waves detected by the apparatus is given by

fr = f((1+v/u)/(1-v/u))

[Hint: There are two Doppler shifts. A red blood cell first acts asa moving observer; then it acts as a moving source when itreradiates the reflected sound at the same frequency that itreceived.]

Explanation / Answer

when the cell receive. f1=f*(1+v/u). ------- when the receiver receive the signal from the cell. fr=f1/(1-v/u) so that fr=f1*(1+v/u)/(1-v/u)

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