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Ultrasound in Medicine. 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 72 beats per second are detected. The speed of sound in body tissue is 1500 m/s. Calculate the speed of the fetal heart wall at the instant this measurement is made.

Sagot :

The speed of the fetal heart wall at the instant is 0.031 m/s when 72 beats per second of hart beat was detected.

The Doppler Effect, defined as the change in frequency of a wave in relation to an observer moving relative to the wave source, must be used.

Let

v= magnitude of the heart wall speed

V= speed  of sound = 1500

fh= the frequency the heart receives (and  reflects) =

fi= original frequency

ff= reflected frequency

fb= frequency for the beats=72

Make use of the Doppler Effect formula.

We have this formula because the heart is a moving observer and the device is a stationary source.

[tex]f_h = [(V+ v)/(v)] fi....(1)[/tex]

We can use this formula if we consider the heart to be a moving source and the device to be a stationary observer.

[tex]f_f = [(V)/(V-v)] fh....(2)[/tex]

The beats' frequency would be the difference between the original and reflected frequencies.

[tex]f_b = f_f -f_i......(3)[/tex]

substituting (1) and (2) into (3),

[tex]f_b=\frac{V}{V-v}\frac{V+v}{V}f_i-f_i\\\\f_b=f_i(\frac{V+v}{V-v}-1)\\\\f_b=f_i\frac{V+v-V+v}{V-v}\\\\f_b=\frac{2v}{V-v}[/tex]

solving for v ,

[tex]v=V\frac{f_b}{2f_i-f_b}=1500\frac{72}{2(1.70*10^6)-72}=0.031 m/s[/tex]

Thus, the speed of fetal heart is 0.031 m/s

To learn more about doppler effect refer here

https://brainly.com/question/15318474

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