Physics
LO4-Lec2-Homework Due in Recitation Class,
Name
Doppler ultrasound is commonly used to assess the health of
blood vessels. As shown, the probe emits and receives
ultrasonic waves. The emitted waves reflect off surfaces
where there is a difference in acoustical impedance. The
reflected waves are detected by the receiver, which converts
the sound energy into electrical signals that are then
analyzed. If the object causing reflection is moving, the
frequency of the reflected wave will be different from that
of the incident wave. This Doppler shift is given by
f = 2f t v cos /c
where f is the Doppler shift in frequency , ft is the
transmitted frequency, v is the velocity of the reflecting
surface,  is the angle between the path of the sound and the
blood vessel, and c is the speed of sound in the tissue.
1. Given that f t is 5 MHz,  is 60o , c is 1500 m/s, and f is 1.60 kHz, what is the velocity of blood inside the
vessel in the diagram above?
2. If it takes 100 s for sound to reach the vessel and return to the probe, how far is the vessel from the probe?
3. The instrument is used to assess another vessel and no Doppler shift is detected. Possible reasons for this are:
I. A vessel has not been located.
II. There is no blood flow in the vessel.
III.  is 90o
IV.  is so large that there is excessive refraction and reflection at tissue boundaries.
Circle the correct response:
A. I and II are correct
C. All are correct
B. I, II, and III are correct
D. I, II, and IV are correct
4.. Doppler ultrasound, although useful for assessing large vessels and those near to the skin, is still difficult to
use for relatively small vessels deep in the body such as the coronary arteries. A possible solution to this
problem is the injection of a contrast agent into the blood that will reflect the sound waves better than red blood
cells do. Supposing it were possible to have an agent that actually emitted ultrasound instead of just reflecting it.
In such a case, what would the equation for the Doppler shift, f, be? Show your derivation.
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