With f0 = 5 MHz, c = 1540 m/s, θ = 60°, and target velocity v = 0.5 m/s, what is the Doppler frequency shift fD?

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Multiple Choice

With f0 = 5 MHz, c = 1540 m/s, θ = 60°, and target velocity v = 0.5 m/s, what is the Doppler frequency shift fD?

Explanation:
Doppler frequency shift in ultrasound comes from motion of the scatterer and is given by fD = 2 f0 v cos θ / c. The factor 2 accounts for the wave traveling to the moving target and back, and cos θ accounts for the angle between the target’s velocity and the beam direction. Plugging in the numbers: cos 60° = 0.5, so fD = (2 × 5,000,000 Hz × 0.5 × 0.5) / 1540 m/s = (2.5 × 10^6) / 1540 ≈ 1,623 Hz ≈ 1.62 kHz. Thus the Doppler shift is about 1.62 kHz. Note that at θ = 0 (motion directly toward the beam) the shift would be larger (about 3.25 kHz), illustrating how the angle reduces the observed shift.

Doppler frequency shift in ultrasound comes from motion of the scatterer and is given by fD = 2 f0 v cos θ / c. The factor 2 accounts for the wave traveling to the moving target and back, and cos θ accounts for the angle between the target’s velocity and the beam direction.

Plugging in the numbers: cos 60° = 0.5, so fD = (2 × 5,000,000 Hz × 0.5 × 0.5) / 1540 m/s = (2.5 × 10^6) / 1540 ≈ 1,623 Hz ≈ 1.62 kHz.

Thus the Doppler shift is about 1.62 kHz. Note that at θ = 0 (motion directly toward the beam) the shift would be larger (about 3.25 kHz), illustrating how the angle reduces the observed shift.

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