Expectant mothers many times see their unborn child for the first time during an

Question

Expectant mothers many times see their unborn child for the first time during an ultrasonic examination. In ultrasonic imaging, the blood flow and heartbeat of the child can be measured using an echolocation technique similar to that used by bats. For the purposes of these questions, please use 1500 m/s as the speed of sound in tissue.

PART B.Blood flow rates in the umbilical cord can be found by measuring the Doppler shift of the ultrasound signal reflected by the red blood cells. If the source emits a frequency f, what is the measured reflected frequency fR? Assume that all of the red blood cells move directly toward the source. Let c be the speed of sound in blood and v be the speed of the red blood cells.

f(c+v)vc

f(c+v)cv

f(c+v)c

f(cv)v+c

Explanation / Answer

From Doppler effect,

frequency heared then emited by the blood particles,

fb=(c+v)f/c    ......eq(1)

frequency heared back from the source

fr=fbc/(c-v)    .......eq(2)

eq(1) is substitute in eq(2)

then fr=[(c+v)f/c][c/(c-v)]

after simplification

fr=f(c+v)/(c-v)

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