State the Doppler shift equation used in ultrasound to determine blood speed.

Δf = 2fv cos θ / c, where Δf is the frequency shift, f is the transmitted frequency, v is blood velocity, θ is the angle between the beam and blood flow, and c is the speed of ultrasound.

In the Doppler ultrasound equation, what does the angle θ represent?

The angle between the ultrasound beam direction and the direction of blood flow.

State the rearranged Doppler equation for calculating blood velocity.

v = cΔf / (2f cos θ), where v is blood velocity, c is the speed of ultrasound, Δf is the frequency shift, f is the transmitted frequency, and θ is the angle between the beam and blood flow.

Calculate the blood speed when speed of ultrasound in tissue = 1550 m s⁻¹, frequency shift = 1100 Hz, transmitted frequency = 5.8 × 10⁶ Hz, cosine of angle = 0.75.

Blood speed = (1550 × 1100) ÷ (2 × 5.8 × 10⁶ × 0.75) = 0.196 m s⁻¹.

Why does a factor of 2 appear in the Doppler equation for ultrasound blood flow measurement?

Because the ultrasound undergoes a frequency shift both when approaching the moving blood cells and when reflecting back from them.

OCR A-Level Physics A H556

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Doppler ultrasound

2 things to know
Papers 1, 2 and 3

Overview

Recall questions on the Doppler effect in ultrasound, the Doppler equation for blood speed with calculations, the factor of 2 and why the beam must be angled to the blood flow.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Key term

In Doppler ultrasound, what does the angle θ represent and what is the Doppler effect, and how does coupling gel reduce reflection at the skin?

Key term

What is the Doppler effect in the context of ultrasound imaging?

Questions from this subtopic

Each one with the model answer underneath.

1
What is the Doppler effect in the context of ultrasound imaging?
Model answer
The change in frequency of ultrasound waves reflected from moving objects, such as blood cells.
2
State the Doppler shift equation used in ultrasound to determine blood speed.
Model answer
Δf = 2fv cos θ / c, where Δf is the frequency shift, f is the transmitted frequency, v is blood velocity, θ is the angle between the beam and blood flow, and c is the speed of ultrasound.
3
In the Doppler ultrasound equation, what does the angle θ represent?
Model answer
The angle between the ultrasound beam direction and the direction of blood flow.
4
State the rearranged Doppler equation for calculating blood velocity.
Model answer
v = cΔf / (2f cos θ), where v is blood velocity, c is the speed of ultrasound, Δf is the frequency shift, f is the transmitted frequency, and θ is the angle between the beam and blood flow.
5
Calculate the blood speed when speed of ultrasound in tissue = 1550 m s⁻¹, frequency shift = 1100 Hz, transmitted frequency = 5.8 × 10⁶ Hz, cosine of angle = 0.75.
Model answer
Blood speed = (1550 × 1100) ÷ (2 × 5.8 × 10⁶ × 0.75) = 0.196 m s⁻¹.
6
Why does a factor of 2 appear in the Doppler equation for ultrasound blood flow measurement?
Model answer
Because the ultrasound undergoes a frequency shift both when approaching the moving blood cells and when reflecting back from them.

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