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.

fR = f (c + v) / c

Explanation:

The speed of a wave is its frequency x wavelenght. Therefore,

Frequency is speed of wave over the wavelength.

Since the source (ultrasound machine) is stationary, and the receiver red blood cell is moving towards it. The wavelenght of the wave sent out towards the observer is c/f

The speed of the reflected sound wave is (c + v), so that the reflected frequency fR is given by

fR = f (c + v) / c