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 detector that produces beeps of audible sound in synchronization with the fetal heartbeat. Suppose the fetus's ventricular wall moves in simple harmonic motion with an amplitude of 1.85 mm and a frequency of 160 beats per minute.

(a) Find the maximum linear speed of the heart wall. Suppose a source mounted on the 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. m/s

(b) Find the maximum change in frequency between the sound that arrives at the wall of the baby's heart and the sound emitted by the source. Hz

(c) Find the maximum change in frequency between the reflected sound received by the detector and that emitted by the source. Hz

Explanation / Answer

solution:

a). w = 2*pi*f = 2pi*160/60 = 16.75 rad/s

vmax = Aw = 1.85*10^-3 * 16.75 = 31 *10^-3 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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