7. The Doppler effect can be used to determine the speed of red blood cells (as

Question

7. The Doppler effect can be used to determine the speed of red blood cells (as wel as baseballs and cars). The Doppler speed detector emits sound at a particular frequency and detects the reflected sound at a different frequency. The difference in the emitted and detected sound frequencies indicates the speed of the object being measured. Assume that sound of frequency 100,000 Hz enters an artery opposite the direction of blood flow, which travels at speed 0.40 m/s. Answer the questions below to see how detecting the frequency of the sound reflected from a red blood cell indicates how fast it is moving a. Use the Doppler equation to determine the frequency that the cell would detect as it moves toward the sound source b. Suppose that the moving cell emits sound at the same frequency it detected in part a. What frequency does the Doppler detection system measure coming from the cell? c. Often the Doppler detection system measures a beat frequency. The beat frequency is the magnitude of the difference between the emitted sound frequency and the reflected sound trequency that it received back from the moving blood cell. What beat frequency is observed in the case described above?

Explanation / Answer

7. given sound frequency from the source, fo = 100,000 Hz

speed of blood flow ub = 0.4 m/s

a. from doppler's equation

frequency seen by RBC as it movces towards the source = f'

f' = fo*(v + ub)/v

here v is speed of sound in blood = 1540 m/s

hence

f' = 100025.9740259740 Hz

b. frequency detectro's detected frequency = f"

f" = f'*v/(v - ub) = 100051.96154845 Hz

c. beat frequency = f" - f = 100051.96154845 - 100,000 = 51.9615484541439 Hz

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