Question

If the velocity of blood flow in the aorta is normally about 0.32 m/s, what beat frequency would you expect if 4.40-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of 1540 m/s .

Answer 1

Answer:

The beat frequency is 0.0019 MHz.

Explanation:

Given that,

Velocity = 0.32 m/s

Frequency = 4.40 MHz

Speed of wave = 1540 m/s

We need to calculate the frequency

Case (I),

Observer is moving away from the source

Using Doppler's effect

$f'=\dfrac{v-v'}{v}f$

Where, v' = speed of observer

Put the value into the formula

$f'=\dfrac{1540-0.32}{1540}\times4.40$

$f'=4.399\ MHz$

Case (II),

Cell is as the source of sound of frequency f' and it moving away from the observer.

Using formula of frequency

$f''=\dfrac{v-v_{s}}{v+v_{s}}\times f$

$f''=\dfrac{1540-0.32}{1540+0.32}\times4.399$

$f''=4.3971\ MHz$

We need to calculate the beat frequency

$\Delta f= f'-f''$

$\Delta f=4.399-4.3971=0.0019\ MHz$

Hence, The beat frequency is 0.0019 MHz.