Physics, 23.03.2020 23:53 htxalyssa

If the velocity of blood flow in the aorta is normally about 0.32 m/s, what beat frequency would you expect if 4.30-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of 1.54 x 10^3 m/s.

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Answer from: teescub9738

The beat frequency is $\Delta f = 0.0011$

Explanation:

From this question we are given that

The velocity blood flow is v = 0.32 m/s

The velocity of the wave is v_w = 1.54*10^3 m/s

The frequency of the ultrasound is f= 4.30MHz

During the time it is been directed along flow the blood cell is moving away frequency of the ultrasound wave(f) hence we are going to employ the Doppler's effect to obtain the frequency

$f' = \frac{v_w-v}{v_w} f$

$= \frac{1.540 *10^3 -0.32}{1.540*1063} *4.30MHz = 4.2991MHz$

When the red blood cell reflects the wave in this case the source of the wave is the blood cells and its frequency() is moving away from the observer (blood cells) and this case the Doppler's effect is mathematically given as

$f'' = \frac{v_w}{(v_w +v)}f$

$= \frac{v_w}{v_w +v} *\frac{(v_w - v)}{v}f$

$= \frac{(v_w - v)}{v_w+v }f$

$= \frac{(1.540*10^3 -0.32)}{.54*10^3 + 0.32 } *4.30MHz$

=4.2982 MHz

The beat frequency is mathematically represented as

$\Delta f = f'' -f' = 4.2991 - 4.2982$

=0.0011MHz

Answer from: Quest

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Answer from: Quest

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If the velocity of blood flow in the aorta is normally about 0.32 m/s, what beat frequency would you...