An ambulance screams higher as it races toward you, then drops the instant it passes. The pitch never changed at the source — but a moving source runs into its own sound ahead (bunching the waves, raising the pitch) and outruns it behind (stretching them, lowering it). Slide the speed and hear the siren swing.
For a source moving through still air at speed v, the frequency you hear is f′ = f·c/(c − v) as it approaches and f·c/(c + v) as it recedes, with c ≈ 343 m/s the speed of sound. The wavefronts pile up in front and spread out behind — the same geometry that red-shifts distant galaxies and lets radar clock your car. A fail-loud self-check throws unless an approaching source raises the pitch above 440 Hz and a receding one lowers it below.
Non-relativistic, still air, source moving (observer-moving gives a slightly different form); real sirens add reflections, wind, and the source’s own spectrum. The c/(c±v) shift is exact for this idealisation.