Dopplervelocity

Doppler velocity is the velocity component of an object along the line of sight inferred from the Doppler shift of a wave. When a source and observer move relative to each other, the frequency of the received wave changes; this shift is proportional to the radial velocity for speeds small compared to the wave speed. The term is used for light, sound, and radio waves and is essential in measuring motion in astronomy, medicine, and meteorology.

Relationship: In the non-relativistic regime for light, the fractional frequency shift satisfies Δf/f ≈ - v_r / c, where v_r is the radial velocity toward the observer. The full relativistic expression is f' = f0 sqrt((1+β)/(1-β)) with β = v_r/c. For sound-based Doppler systems, the shift depends on the speed of sound in the medium; in Doppler ultrasound, Δf = 2 f0 v cos θ / c, where θ is the beam angle and c the speed of sound in tissue.

Applications: In astronomy, radial velocity measurements from spectral lines reveal orbital motions, galaxy rotation, and exoplanets. In meteorology, Doppler radar measures the line-of-sight velocity of precipitation. In medicine, Doppler ultrasound estimates blood flow velocity and direction.

Limitations: Doppler velocity yields only the line-of-sight component; the angle must be known to infer total velocity. Instrumental resolution, sampling (aliasing), and spectral broadening limit accuracy. The term originated with Christian Doppler, who described the effect in 1842; contemporary use spans many wavelengths and modalities.

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