(***THIS IS MY THIRD POST FOR THIS QUESTION AND THE PREVIOUS TWO ANSWERS I GOT W

Question

(***THIS IS MY THIRD POST FOR THIS QUESTION AND THE PREVIOUS TWO ANSWERS I GOT WERE WRONG, SO LETS TRY AGAIN PLEASE!!!***)

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

If v is the heart wall speed , V is a speed of sound and fh is the frequency that heart receives( at same time reflect same frequency) , fo is original frequency and fr reflectrd frequency

Consider heart is moving observer and device is stationary source.then the frequency that heart receives is given by

fh =[ (V +v )/v ] fo   -------------------------(1)

Now consider the reflect sound from the heart. Here consider heart is moving source and device is stationary observer.The reflectrd frequency of sound is given by

fr =[ v/(V-v) ] fh   --------------------------(2)

from (1) replace value of  fh in above equation

    fr =[ v/(V-v) ] [ (V +v )/v ] fo

fr =[(V+v) /(V-v) ]  fo -------------------------(3)

Number of beats obtained from the difference in frequency of original ( fo) to the frequency of reflected sound (fr)

Beats (fb) = fr - fo here replace  fr with expression in (3)

fb =[(V+v) /(V-v) ] fo - fo   = fo [{(V+v) /(V-v)} -1] = [2v /(V-v)] fo

  fb =[2v /(V-v)] fo

from above equation find the expression for v we get

v = V [ fb / (2fo + fb )] ------------------------(4)

here V =The speed of sound in body tissue =1500 m/s

fo =intial frequency of sound = 1.70 MHz = 1.70 x106 Hz

fb =85 beats /s =85 Hz

substitude above values in (4)

v = (1500 m/s) [ 85 Hz /( 2 x 1.70 x106 Hz + 85 Hz)]

v =0.037499062 m/s =3.750 cm/s

therefore the speed of the fetal heart wall is 3.750 cm/s

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