For pulsed-wave Doppler with PRF = 12 kHz, f0 = 5 MHz, θ = 60°, find the maximum measurable velocity without aliasing (assume c = 1540 m/s).

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Multiple Choice

For pulsed-wave Doppler with PRF = 12 kHz, f0 = 5 MHz, θ = 60°, find the maximum measurable velocity without aliasing (assume c = 1540 m/s).

Explanation:
In pulsed-wave Doppler, the Doppler frequency shift is fD = (2 f0 v cos θ) / c. The instrument can measure Doppler shifts up to ±PRF/2 without aliasing, so the maximum unaliased fD is PRF/2. Setting fD = PRF/2 and solving for v gives v_max = (PRF/2) · c / (2 f0 cos θ) = (PRF · c) / (4 f0 cos θ). Plugging in the values: PRF = 12 kHz, c = 1540 m/s, f0 = 5 MHz, θ = 60° (cos 60° = 0.5): v_max = (12000 · 1540) / (4 · 5,000,000 · 0.5) = 18,480,000 / 10,000,000 ≈ 1.85 m/s. So the maximum measurable velocity without aliasing is about 1.85 m/s.

In pulsed-wave Doppler, the Doppler frequency shift is fD = (2 f0 v cos θ) / c. The instrument can measure Doppler shifts up to ±PRF/2 without aliasing, so the maximum unaliased fD is PRF/2. Setting fD = PRF/2 and solving for v gives v_max = (PRF/2) · c / (2 f0 cos θ) = (PRF · c) / (4 f0 cos θ).

Plugging in the values: PRF = 12 kHz, c = 1540 m/s, f0 = 5 MHz, θ = 60° (cos 60° = 0.5):

v_max = (12000 · 1540) / (4 · 5,000,000 · 0.5) = 18,480,000 / 10,000,000 ≈ 1.85 m/s.

So the maximum measurable velocity without aliasing is about 1.85 m/s.

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