The angle between the motion and the ultrasound beam enters into the Doppler shift calculation as which trigonometric function?

The angle between the motion and the ultrasound beam enters into the Doppler shift calculation as which trigonometric function?

• A. average
• B. cosine
• C. sine
• D. tangent

Answer: (B)

The Doppler shift depends on the motion component that is along the ultrasound beam. The velocity along the beam is the actual velocity times the cosine of the angle between the flow direction and the beam (radial velocity). In the Doppler equation, this appears as the cosθ term, so the shift is proportional to v cosθ. If the flow is along the beam (θ = 0), cosθ = 1 and you get the maximum shift; if the flow is perpendicular to the beam (θ = 90°), cosθ = 0 and there’s no Doppler shift. Sine would represent the component perpendicular to the beam, which doesn’t contribute to the Doppler shift, and tangent isn’t used here because the relationship is about the projection along the beam, not a ratio of components. In practice, angle correction is essential for accurate velocity measurements, and accuracy worsens as θ approaches 90°.

The Doppler shift depends on the motion component that is along the ultrasound beam. The velocity along the beam is the actual velocity times the cosine of the angle between the flow direction and the beam (radial velocity). In the Doppler equation, this appears as the cosθ term, so the shift is proportional to v cosθ. If the flow is along the beam (θ = 0), cosθ = 1 and you get the maximum shift; if the flow is perpendicular to the beam (θ = 90°), cosθ = 0 and there’s no Doppler shift. Sine would represent the component perpendicular to the beam, which doesn’t contribute to the Doppler shift, and tangent isn’t used here because the relationship is about the projection along the beam, not a ratio of components. In practice, angle correction is essential for accurate velocity measurements, and accuracy worsens as θ approaches 90°.