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Expectant parents are thrilled tohear their unborn baby\'s heartbeat, revealed b

ID: 2264822 • Letter: E

Question

Expectant parents are thrilled tohear their unborn baby's heartbeat, revealed by an ultrasonicmotion detector. Suppose the fetus's ventricular wall moves insimple harmonic motion with amplitude 1.90 mm and frequency 106 beats per minute. Find the maximum linear speed of the heart wall. Suppose the motion detectorin contact with the mother's abdomen produces sound at precisely 2MHz, which travels through tissue at 1.50 km/s. Find the maximum frequency at which soundarrives at the wall of the baby's heart. (Answer to sevensignificant figures.)

Explanation / Answer

A. w = 2pi*101/60 = 10.5767 rad/s
vmax = Aw = 0.019038 m/s
B. f = f0*(c+vr)/c = 2000025.384 Hz
C. f = f0*(c+vr)/c * c/(c-vr) = 2000050.76864436 Hz

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