Doppler Effect Calculator

You set directions explicitly. "Toward" means moving toward the other party (which raises the pitch), "away" lowers it, and "stationary" contributes nothing. The math uses f′ = f (v + v_o) / (v − v_s) with the signs chosen from your selections.

If the source moves at or faster than the wave speed, the term (v − v_source) is zero or negative and the classical formula no longer applies — the source is breaking the sound barrier, producing a shock wave such as a sonic boom.

It uses the classical (non-relativistic) Doppler formula, which is accurate for sound and for slow-moving sources. The relativistic Doppler effect for light at high speeds needs a different equation.

Because sound travels in a medium, and the two cases differ in what happens to the wave itself. A moving source compresses the waves it emits, shortening their wavelength before they reach anyone; a moving observer meets unchanged waves more often. The formulas are therefore not symmetric, and the difference grows as either speed approaches the speed of sound — which is where the source case runs away and the observer case does not.

Yes, because the medium is what carries the wave: a tailwind effectively raises the speed of sound relative to the ground and a headwind lowers it, which shifts the pitch and also bends the path. That is why the same siren carries differently on different days, and why an outdoor measurement that ignores air movement and temperature will not match the calculated figure exactly.