An important characteristic of the heart, one used to diagnose heart disease, is the pressure difference between the blood pressure inside the heart and the blood pressure in the aorta, the large artery leading away from the heart. The blood inside the heart is essentially at rest, but it speeds up significantly as it enters the aorta—and its speed can be measured by using the Doppler shift of reflected ultrasound.

a. The Doppler effect enters twice in calculating the frequency of the reflection from a moving object. Suppose the object’s speed v₀ is very small compared to the wave speed v. Show that a good approximation for the Doppler shift—the difference between the reflected frequency and the incident frequency—is

b. A doctor using 2.5 MHz ultrasound measures a 6000 Hz Doppler shift as the ultrasound reflects from blood ejected from the heart into the aorta. What is the blood pressure difference, in mm of Hg, between the inside of the heart and the aorta? Assume the patient is lying down so that there is no height difference between the heart and the aorta. The density of blood is 1060 kg/m³.

Transcribed Image Text:

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