Blood flow rates in the umbilical cord can be found by measuring the Doppler shift of the ultrasound signal reflected by the red blood cells. If the source emits a frequency f, what is the measured reflected frequency fR? Assume that all of the red blood cells move directly toward the source. Let c be the speed of sound in blood and v be the speed of the red blood cells.
A) f (c+v)/c
B) f (c+v)/c-v
C) f (c+v)/v-c
D) f (c-v)/v+c
fb = frequency heard then emmitted by blood particle
fb = (c+v) f /c
fl = frequency heard back at the source
f receiver = fr = fb c/(c-v)
so the result is:
fr = f * (c+v)/(c-v)
which is B (sort of, parenthesis missing)
D) f (c-v)/v+c
The correct option is A) f (c+v)/c.
The Doppler shift formula for a moving source towards the observer is given by:
fR = f ((c+v) / c)
Where:
fR is the measured reflected frequency
f is the emitted frequency by the source
c is the speed of sound in blood
v is the speed of the red blood cells
This formula accounts for the fact that the reflected frequency will be higher when the red blood cells are moving towards the source.
To determine the measured reflected frequency using the Doppler shift, we can use the formula:
fR = f (c + v) / (c + v)
In this case, the source emits a frequency f, the speed of sound in blood is c, and the speed of the red blood cells is v.
So, the correct answer is A) f (c + v) / c.