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

Answer:

$\Delta f=17959.2\ Hz$

Explanation:

Given:

• original frequency of  the wave, $f=4.4\times 10^6\ Hz$

• velocity of the blood stream moving away, $v=1.4\ m.s^{-1}$

Doppler shift is given as:

$\frac{f}{f_o} =\frac{s+v_s}{s-v_o}$

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

$\frac{4.4\times 10^6}{f_o} =\frac{1570+0}{1570-1.4}$

$f_o=4396076.43\ Hz$

Therefore the shift in frequency:

$\Delta f=f-f_o$

$\Delta f=3923.56\ Hz$