The Doppler effect

A source emitting sound at a fixed frequency sends out wave crests at perfectly regular intervals. If the source is moving toward a listener, each successive crest is emitted from a position slightly closer than the last, so crests arrive at the listener more closely spaced in time than they were emitted — the listener perceives a higher frequency, a higher pitch, even though the source's own vibration never sped up. Moving away has the opposite effect: crests are emitted from increasingly distant points, arrive more spread out in time, and the listener hears a lower pitch. Nothing about the wave itself has changed; what changed is the timing of arrival, because the source's motion during the interval between successive crests shifts where each one starts its journey.

This is why a passing ambulance siren drops in pitch specifically at the moment it passes, not gradually before or after: the frequency shift depends on the relative velocity along the line connecting source and observer, which is maximal (source directly approaching or receding) right at closest approach in a typical flyby geometry and decreases as the source moves off to the side.

The effect is genuinely present for a moving source and for a moving observer, but the two cases are not identical in their exact formula, even though the qualitative direction of the shift is the same either way — a subtlety that matters for sound because sound has a definite medium (air) to be at rest with respect to, giving source motion and observer motion distinguishable roles. The same underlying idea applies well beyond sound: light from a receding galaxy is redshifted by the same essential mechanism, which is how the expansion of the universe is measured, and it is why police radar guns and medical ultrasound both use Doppler shifts to measure speed.