A 2.00-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. Calculate the speed of the fetal heart wall at the instant this measurement is made.
Text Solution
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Let f 0 = 2.00 MHz be the frequency of the generated wave. The frequency with which the heart wall receives this wave is f H = 
f 0 , and this is also the frequency with which the heart wall re-emits the wave. The detected frequency of this reflected wave is f' 
, f H , with the minus sign indicating that the heart wall, acting now as a source of waves, is moving toward the receiver. Combining, f' 
f 0 , and the beat frequency is
f beat = f' – f 0 = 
f' = 
f 0 .
Solving for v H ,
v H = v 
= (1500 m/s)
Note that in the denominator in the final calculation, f beat is negligible compared to f 0 .
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