The same effect that causes the change in pitch of a siren as it drives past is also used to estimate blood flow with ultrasound, measure the speed of a passing car, and even determine the motion of the stars. Doppler shift-based satellite navigation was also the first operational use of a system that eventually led to GPS.
When a regular pitched siren or similar approaches I try to imagine the crunching up of the sound waves — the vehicle seemingly chasing after its own sound — and the stretching out of the waves as it heads past and into the distance. At least it makes it less painful on the ears.
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