Doppler ultrasound is used to measure the speed of blood flow. If the speed of t

Question

Doppler ultrasound is used to measure the speed of blood flow. If the speed of the red blood cells is v, the speed of sound in blood is u, the ultrasound source emits waves of frequency f, and we assume that the blood cells are moving directly toward the ultrasound source, then the frequency fr of reflected waves detected by the apparatus is given by the formula below.

The reflected sound interferes with the emitted sound, producing beats. If the speed of red blood cells is 0.14 m/s, the ultrasound frequency used is 5.0 MHz, and the speed of sound in blood is 1570 m/s, what is the beat frequency?

Explanation / Answer

We will use the Doppler eqn

The frequency of the listener fL = fS*(v*vL)/(v+vS) here vL = 0 and vS = 0.10m/s speed of the source

so fL = 5.0x10^6*(1500)/(1500-0.10) = 5000333Hz

So the beat frequency is 5000333 - 5000000 = 333Hz

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