Expectant parents are thrilled to hear their unbron babay\'s heartbeat, revealed

Question

Expectant parents are thrilled to hear their unbron babay's heartbeat, revealed by an ultrasonic detector that produces beeps of audible sound in synchronization with the fetal heartbeat.

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Expectant parents are thrilled to hear their unborn baby's heartbeat, revealed by an ultrasonic detector that produces beeps of audible sound in synchronization with the fetal heartbeat. Suppose the fetus's heart wall moves in simple harmonic motion with amplitude 2.00 mm and a frequency of 115 beats per minute. Calculate the maximum speed of the heart wall. A source is mounted on the detector in contact w ith the mother's abdomen, and produces sound at 2,000,000.0 Hz. The speed of sound in body tissue is 1500 m/s. If the heart wall is moving at its maximum speed toward the sound waves from the source, calculate the difference in frequency between the reflected sound received back at the detector, and the original signal. Show your work, and carefully explain your method of solution and your choice of signs. (Keep lots of significant figures in your intermediate calculations.) Although this difference in frequency is very small compared to that of the ultrasound, it can be easily detected by looking for the beats between the two signals!

Explanation / Answer

a. as we know dat w = 2 pie f

= 2 * 3.14 * 115/60 = 12 rad/sec

also v = wA = 12 * (2*10^-3) = 0.024 m/sec

b. Heart wall is moving observer hence

F' = f (v+vo)/v

2000000

* (1500+0.024)/1500 = 2000032 Hz

c. here heart wall is moving source

f' = 2000032 * 1500/ (1500- 0.024) = 2000064.001 hZ

Now hope its clear........

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