Why does the sound of emergency sirens change as you pass them by?

This effect is called Doppler Shift. What does that mean, you ask. Well...

When the source of the waves, in this case the siren, is moving toward the observer, each successive wave is emitted from closer to the observer than the previous wave. Each wave takes less time to reach the observer than the previous wave and thus the time between the arrivals of successive wave crests are reduced, causing an increase in the frequency.

If the source of waves is moving away from the observer, each wave is emitted farther from the observer than the previous wave, so the arrival time between each wave is increased, reducing the frequency.

This is also the case when a car passes you by; you get a higher pitch on the approach, followed by a lower pitch noise as it has passed you by.

It sounds like (taking a deep breath for childish noise time...) NEEEEEEEVVVOOOOOOOOOOMMMM