Ultrasound has many medical applications, one of which is to monitor fetal heart

Question

Ultrasound has many medical applications, one of which is to monitor fetal heartbeats by reflecting ultrasound off a fetus in the womb. If the surface if the heart is moving, the reflected ultrasound—an echo—is Doppler shifted. Suppose the emitted frequency is f0 nd the Doppler-shifted reflected frequency is fecho. Because fechof0, microphone that listens to both frequencies simultaneously will detect a beat frequency. If the reflecting object's speed vo is much less than the speed of sound, one can show that fbeat(2vo/vsound)f0. Part A The reflection of 2.34 MHz ultrasound waves from the surface of a fetus's beating heart is combined with the 2.34 MHz wave to produce a beat frequency that reaches a maximum of 70 Hz . What is the maximum speed of the surface of the heart? The speed of ultrasound waves within the body is 1540 m/s. Express your answer with the appropriate units. Part B Suppose the surface of the heart moves in simple harmonic motion at 90beats/min. What is the amplitude in mm of the heartbeat?

Explanation / Answer

Fbeat = 2 * Vt/Cs * fo

V tissue = Cs * fbeat /2 fo

V tissue = 70 * 1540/(2 * 2.34 e 6)

Vtissue = 0.023 m/s

-----------------------------------------

W = 90 beats / min = 90 /60 = 1.5 beats/s

Speed V = Rmax W

Rmax = V/W = 0.023/(1.5

Rmax = 0.0153 m is the amplitude of heartbeat

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