A 1.70 MHz sound wave travels through a pregnant woman\'s abdomen and is reflect

Question

A 1.70 MHz sound wave travels through a pregnant woman's abdomen and is reflected from the fetal heart wall of her unborn baby. The heart wall is moving toward the sound receiver as the heart beats. The reflected sound is then mixed with the transmitted sound, and 85 beats per second are detected. The speed of sound in body tissue is 1500 m/s.

Part A

Calculate the speed of the fetal heart wall at the instant this measurement is made.

Express your answer in centimeters per second to three significant figures.

Explanation / Answer

f = 1.70 * 10^6 Hz
Speed of sound in body tissue, = 1500 m/s

The freq with which Heart wall the wave, fh = fo * (v + vh)/v
this is also the frequency with which the heart wall re-emits the wave, so
f' = fh * (v)/(v - vh)

Now combining f’ =  fo * (v + vh)/ (v) * (v)/(v - vh)
f' =  fo * (v + vh)/(v - vh)
beat frequency = f' - fo
beat frequency =  fo * (v + vh)/(v - vh) - fo

Substituing Values,
85 = 1.70 * 10^6 * [ (1500+vh)/(1500 - vh) - 1]
vh = 3.75 * 10^-2 m/s
Speed of the fetal heart wall, vh = 3.75 * 10^-2 m/s

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