Doppler effect
Why does an ambulance siren sound higher as it approaches and lower as it moves away? Move the source, listen to the change and break the sound barrier.
What is the Doppler effect?
A sound source emits waves that travel away from it in all directions at the speed of sound. If the source moves, each new wavefront starts from a point a little further ahead: in front of it the fronts bunch up (shorter wavelength, higher pitch) and behind it they spread out (longer wavelength, lower pitch). Christian Doppler described it in 1842.
f' = f · c / (c ∓ v)
where f is the emitted frequency, c the speed of sound in the medium and v the speed of the source; the minus sign is for an observer the source is approaching and the plus sign for one it is moving away from. An ambulance at 100 km/h (62 mph, 28 m/s) with a 440 Hz siren is heard at about 479 Hz as it approaches and about 407 Hz as it moves away: almost three semitones apart.
The sound barrier and the Mach cone
When the source reaches the speed of sound (Mach 1), the wavefronts pile up right in front of it. If it goes even faster, it leaves its own waves behind and they form a Mach cone, whose half-angle satisfies sin θ = c / v. That cone is the shock wave we hear as a sonic boom when a supersonic aircraft flies past.
Not just sound
The Doppler effect is used in police speed radars, in ultrasound scans to measure blood flow and in astronomy: light from receding galaxies arrives shifted towards red, one of the pieces of evidence that the universe is expanding.
Frequently asked questions
What is the Doppler effect formula?
For sound, f′ = f · (v + vo) / (v − vs), where v is the speed of sound (about 343 m/s in air at 20 °C), vo is the speed of the observer towards the source and vs the speed of the source towards the observer. If either one moves away, its speed is taken as negative.
Why does an ambulance siren change pitch as it passes?
As it approaches, the waves arrive closer together and we hear a higher pitch; as it moves away, they arrive further apart and it sounds lower. A 700 Hz siren at 90 km/h (25 m/s) is heard at about 755 Hz while approaching and about 652 Hz while receding: a jump of more than two semitones right as it passes.
What is the redshift of galaxies?
It is the Doppler effect applied to light. When a galaxy moves away from us, its light arrives with a longer wavelength, shifted towards red. In 1929 Edwin Hubble observed that the farther away a galaxy is, the larger its redshift, the first evidence that the universe is expanding.
What is the Doppler effect used for?
Traffic radars measure car speeds from the frequency shift of the reflected wave. Doppler ultrasound measures blood flow in veins and arteries, weather radars detect wind inside storms, and astronomers use it to discover planets orbiting other stars.