Question

An echocardiogram uses 4.4 MHz ultrasound to measure blood flow in the aorta. The blood is moving away from the probe at 1.4 m/s. What is the frequency shift of the reflected ultrasound?

Answer 1

`\Delta f=17959.2\ Hz`

Step-by-step explanation:

Given:

• original frequency of the wave,
  `f=4.4* 10^6\ Hz`

• velocity of the blood stream moving away,
  `v=1.4\ m.s^(-1)`

Doppler shift is given as:

`(f)/(f_o) =(s+v_s)/(s-v_o)`

where:

s = velocity of ultrasound in blood =
`1570\ m.s^(-1)`

`v_s=` velocity of sound source towards the observer

`v_o=` velocity of the observer away from the source

`(4.4* 10^6)/(f_o) =(1570+0)/(1570-1.4)`

`f_o=4396076.43\ Hz`

Therefore the shift in frequency:

`\Delta f=f-f_o`

`\Delta f=3923.56\ Hz`