the Doppler effect
/ DOP-ler /
An ambulance races past you and its siren suddenly drops in pitch, high while it is approaching, low once it has passed. That change in pitch caused by motion is the Doppler effect. The question it answers is: why does a moving sound source change its pitch as it goes by?
The Doppler effect is the change in the observed frequency (and wavelength) of a wave when the source and the observer move relative to each other. As a source approaches, each successive crest is emitted a little closer, so the crests bunch up: shorter wavelength, higher frequency. As it recedes, the crests stretch out: longer wavelength, lower frequency. For sound, the observed frequency is f' = f (v +/- v_o) / (v -/+ v_s), where v is the speed of sound, v_o the observer's speed, and v_s the source's speed, with the signs chosen so that approaching raises the pitch.
The effect works for all waves. Police radar and weather radar use the Doppler shift of reflected radio waves to measure speed, and astronomers see distant galaxies shifted toward longer, redder wavelengths, the redshift, showing that the Universe is expanding. An honest note: for sound the formula treats the source's motion and the observer's motion differently, because they move relative to the air (the medium). But for light there is no medium, so the relativistic Doppler shift depends only on their relative velocity.
An ambulance siren emitting f = 700 Hz approaches you at v_s = 30 m/s (sound speed v = 343 m/s). You hear f' = 700 times 343/(343 - 30), about 767 Hz, while it nears, then a lower pitch once it passes and recedes.
Relative motion bunches or stretches the waves, raising pitch on approach and lowering it on recession.
For sound the source's and the observer's motions enter the formula differently, because they move relative to the air. For light there is no medium, so only the relative velocity matters.