When the heart pumps blood into the aorta, the pressure gradient-the difference between the blood pressure inside the heart and the blood pressure in the artery-is an important diagnostic measurement. A direct measurement of the pressure gradient is difficult, but an indirect determination can be made by inferring the pressure difference from a measurement of velocity. Blood is essentially at rest in the heart; when it leaves and enters the aorta, it speeds up significantly and - according to Bernoulli's equation-the pressure must decrease. A doctor using \(2.5 \mathrm{MHz}\) ultrasound measures a \(6000 \mathrm{~Hz}\) frequency shift as the ultrasound reflects from blood ejected from the heart.

a. What is the speed of the blood in the aorta?

b. What is the difference in blood pressure between the inside of the heart and the aorta? Assume that the patient is lying down and that there is no difference in height as the blood moves from the heart into the aorta.