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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 :

Answer:

[tex]\Delta f=17959.2\ Hz[/tex]

Explanation:

Given:

  • original frequency of  the wave, [tex]f=4.4\times 10^6\ Hz[/tex]
  • velocity of the blood stream moving away, [tex]v=1.4\ m.s^{-1}[/tex]

Doppler shift is given as:

[tex]\frac{f}{f_o} =\frac{s+v_s}{s-v_o}[/tex]

where:

s = velocity of ultrasound in blood = [tex]1570\ m.s^{-1}[/tex]

[tex]v_s=[/tex] velocity of sound  source towards the observer

[tex]v_o=[/tex] velocity of the observer away from the source

[tex]\frac{4.4\times 10^6}{f_o} =\frac{1570+0}{1570-1.4}[/tex]

[tex]f_o=4396076.43\ Hz[/tex]

Therefore the shift in frequency:

[tex]\Delta f=f-f_o[/tex]

[tex]\Delta f=3923.56\ Hz[/tex]

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