Doppler — Source Moving

Doppler effect: apparent frequency of a wave changes when SOURCE moves relative to OBSERVER.

Source moving TOWARD stationary observer: apparent f INCREASES (waves compressed in front).

Source moving AWAY from stationary observer: apparent f DECREASES (waves stretched behind).

Formula (source moves, observer stationary): f' = f × v/(v ∓ v_s). Minus when source approaches.

v_s = source speed; v = wave speed (in medium).

Higher harmonics shift more than fundamental (in relative terms).

If v_s ≥ v: produces a sonic boom (cone of compressed waves at Mach angle θ = sin⁻¹(v/v_s)).

Used in: weather radar (raindrop velocity), police radar (car speed), medical Doppler ultrasound (blood flow), astronomy (redshift of galaxies).