the doppler effect
nothing about the siren changes as it passes you. it emits exactly one pitch the whole time. what changes is that the source keeps chasing the sound it already made — so the waves in front of it get crowded and the ones behind get stretched.
click anywhere to move the listener. put it directly in the path and the pitch drops in an instant instead of sliding.
emitted
400 Hz
heard
400 Hz
shift
0.0 semitones
speed
741 km/h
the shift isn't symmetric. approaching multiplies the frequency by c/(c−v); receding divides by c/(c+v). so the rise on the way in is always bigger than the fall on the way out — that lopsidedness is why a passing siren sounds like it drops off a cliff.
the tone you hear is the shifted one, recalculated every frame from where the source is and how fast it's closing. drag the speed up to mach 1 and the pitch runs away — that's the formula dividing by nearly zero.