frequency shift

Meaning: A frequency shift is the difference between the frequency a detector measures and the frequency the source emits, caused by relative motion of source and detector (the Doppler effect). Moving closer raises the observed frequency; moving apart lowers it. A moving source crowds or stretches wavelengths in the medium; a moving detector meets wavefronts more or less often.

Equation: f' = f (v ± vD)/(v ∓ vS), where f' is the observed frequency (Hz), f is the emitted frequency (Hz), v is the wave speed in the medium (m/s), vD is the detector speed (m/s) and vS is the source speed (m/s). Use the upper signs for approach and the lower signs for separation. For speeds far below v, Δf/f ≈ vrel/v, where vrel is the relative speed (m/s).

On the MCAT: Expect sirens, bats, or ultrasound reflecting from moving objects; for light, redshift means the source is receding. You predict whether f' rises or falls, or compute from the ratio vrel/v. A wave reflected from a moving target is shifted twice, which roughly doubles Δf.

Common confusion: The source's emitted frequency and the wave speed in the medium do not change; only the observed frequency (and, for a moving source, the wavelength) does. Only velocity components along the line joining source and detector count.