.A doppler fetal monitor is a hand-held ultrasound device that is used to detect a fetal heartbeat in prenatal care. The device works by measuring the speed of the fetus's ventricular wall and thereby tracking its heartrate.
a. Suppose the fetus's ventricular wall moves back and forth in a pattern approximating simple harmonic motion with an amplitude of 1.7 mm and a frequency of 3.0 Hz. Find the maximum speed of the heart wall (in m/s) during this motion. Be careful of units!
b. Suppose that the ultrasound source placed on the mother's abdomen produces sound at a frequency 2 MHz (a megahertz is 10^6106Hz). Sound travels through tissue at roughly the same speed as in water (v\approx 1500v≈1500m/s). Find the maximum change in frequency between the sound that is emitted by the device and the sound that is observed at the wall of the baby's heart. Treat the heart wall as a moving observer. Hint: you will need to use your answer from part (a). Give your answer as a positive number in Hz.
c,
Now find the maximum difference in frequency between the ultrasound emitted by the device and the reflected sound received by the device after it bounces off the ventricular wall. This is the frequency shift that the device measures.
Treat the heart wall as a moving source, emitting a wave with the frequency that you found in part (b). Give your answer as a positive number in Hz
