Expectant parents are thrilled to hear their unborn baby\'s heartbeat, revealed

Question

Expectant parents are thrilled to hear their unborn baby's heartbeat, revealed by an ultrasonic motion detector. Suppose the fetus's ventricular wall moves in simple harmonic motion with an amplitude of 1.80 mm and a frequency of 140 per minute.

(a) Find the maximum linear speed of the heart wall. Suppose the motion detector in contact with the mother's abdomen produces sound at 2,000,000.0 Hz which travels through tissue at 1.50 km/s.

The answer is 0.0264 m/s.

(b) Find the difference between the original frequency and the maximum frequency at which sound arrives at the wall of the baby's heart.

Answer in Hertz.

(c) Find the difference between the original frequency and the maximum frequency at which reflected sound is received by the motion detector. By electronically "listening" for echoes at a frequency different from the broadcast frequency, the motion detector can produce beeps of audible sound in synchronization with the fetal heartbeat.

Answer in Hertz.

I will need help with solving b and c. If anyone helps me, I will reward points.

Explanation / Answer

A. w = 2pi*101/60 = 10.5767 rad/s vmax = Aw = 0.026038 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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