How does the incidence angle θ affect the Doppler shift in the Doppler equation?

• A. The Doppler shift is independent of θ.
• B. The Doppler shift is proportional to cos θ, so larger θ reduces fD; at 90°, fD is zero.
• C. The Doppler shift varies with sin θ.
• D. The Doppler shift increases with θ.

Answer: (A)

The Doppler shift in ultrasound depends on how much of the target’s velocity is along the beam direction. That dependence comes through the cos θ factor in the Doppler equation: fD = (2 f0 v cos θ) / c. This means the shift is maximal when the motion is aligned with the beam (θ = 0°) and goes to zero when the motion is perpendicular to the beam (θ = 90°). So the shift is not independent of θ; it scales with cos θ.

The other ideas don’t fit: a dependence on sin θ would imply a different geometric projection, and saying the shift increases with θ would contradict the cos θ dependence.