Doppler Effect

Moving sound source compresses wavefronts ahead, stretches behind — click to place observer

f₀ = 440 Hz | v_source = 0.5 c_sound | f_ahead = 880 Hz | f_behind = 293 Hz

source speed: 0.50c frequency f₀: 440Hz sound speed: 100px/s

The Doppler formula f_obs = f₀/(1 − v·cos θ/c) describes how relative motion shifts perceived frequency. Moving toward an observer compresses wavefronts (blue shift); moving away stretches them (red shift). At v = c, wavefronts pile up to form a Mach cone.