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

Here, apply the principle of doppler effect:

1)Our fixed observer is our ear.
2)Fixed oberver hears lower frequency when the fetal heart beats move away from the observber.
Hence,
f1 =f0(c-v)/c ----------------------1) where fo = incident frequency, fi is the frquency when heard the fetal heart beat away from the heart which is always lower than the source or incident frequency, C is the velocity of sound in tissue and v= velocity of heart wall.
Now ,
85 = 1.70*10^6(1500-v)/(1500 )
or, 50 = 10^6 ( 1500 -v)/(1500)
or, 75000/10^6 = 1500 -v
or v= 1500- 0.075 =1499.92 m/s = 1499.92x10^2 cm/s = 1.4999 x10^5 cm/s

Answer in three significant digit shall be 1.50 x 10^5 cm/s.

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