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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?

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boffeemadrid

Answer:

1300 Hz

Explanation:

f' = Actual frequency = 4.8 MHz

f = Observed frequency

[tex]v_r[/tex] = Relative velocity of blood = 0.21 m/s

v = Velocity of ultrasound = 1540 m/s

From the Doppler effect formula we have

[tex]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[/tex]

Frequency shift is given by

[tex]\Delta f=f-f'\\\Rightarrow \Delta f=4.8013-4.8\\\Rightarrow \Delta f=0.0013\ MHz=1300\ Hz[/tex]

The frequency shift in the sound is 1300 Hz

Lanuel

The frequency shift of the ultrasound reflected from blood is 0.0013 MHz or 1300 Hz.

Given the following data:

  • Frequency of ultrasound = 4.8 MHz
  • Source velocity = 0.21 m/s

Scientific data:

  • Speed of sound = 1540 m/s

To calculate the frequency shift of the ultrasound reflected from blood, we would apply Doppler's effect of sound waves:

The Doppler's effect of sound waves.

Mathematically, Doppler's effect of waves is given by the formula:

[tex]F_o = \frac{V \;+ \;V_s}{V\; - \;V_s} F[/tex]

Where:

  • V is the speed of a sound wave.
  • F is the actual frequency of sound.
  • [tex]V_s[/tex] is the source velocity.
  • [tex]F_o[/tex] is the observer frequency.

Substituting the given parameters into the formula, we have;

[tex]F_o = \frac{1540 \;+ \;0.21}{1540\; - \;0.21} \times 4.8\\\\F_o = \frac{1540.21}{1539.79} \times 4.8\\\\F_o = 1.000027277 \times 4.8\\\\F_o =4.8013 \;MHz[/tex]

For the frequency shift:

[tex]Frequency \;shift = F_o - F\\ \\ Frequency \;shift =4.8013-4.8[/tex]

Frequency shift = 0.0013 MHz or 1300 Hz.

Read more on Doppler's effect here: https://brainly.com/question/3841958

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