Question

A Doppler blood flow unit emits ultrasound at 4.8 MHz. What is the frequency shift of the ultrasound reflected from blood moving in an artery at a speed of 0.21 m/s?

Answer 1

Answer:

1300 Hz

Explanation:

f' = Actual frequency = 4.8 MHz

f = Observed frequency

$v_r$ = Relative velocity of blood = 0.21 m/s

v = Velocity of ultrasound = 1540 m/s

From the Doppler effect formula we have

$f=f'\dfrac{v+v_r}{v-v_r}\\\Rightarrow f=4.8\dfrac{1540+0.21}{1540-0.21}\\\Rightarrow f=4.80130\ Hz$

Frequency shift is given by

$\Delta f=f-f'\\\Rightarrow \Delta f=4.8013-4.8\\\Rightarrow \Delta f=0.0013\ MHz=1300\ Hz$

The frequency shift in the sound is 1300 Hz