Doppler Effect: Definition, Formula and Examples
The Doppler effect is the change in the frequency of a wave when the source of the wave or the observer moves relative to the other. A siren sounds higher-pitched as it comes toward you and lower-pitched as it moves away.
What is the Doppler effect?
When a source moves, it bunches up the wave crests in front of it and stretches them out behind it. Someone in front hears more crests per second, so the observed frequency goes up. Someone behind hears fewer crests per second, so the frequency goes down. The wavelength changes, but the wave speed in the medium does not.
The effect is named after Christian Doppler, who described it in 1842 for light and sound.
Doppler effect formula
For sound, with the source moving and the observer at rest:
f' = f · v / (v ± vs)
- f' is the frequency the observer hears (hertz, Hz)
- f is the frequency the source emits (Hz)
- v is the speed of sound in the medium (343 m/s in air at about 20 °C)
- vs is the speed of the source (m/s)
Use minus (v − vs) when the source moves toward the observer, so the pitch rises. Use plus (v + vs) when it moves away, so the pitch falls.
If the observer moves and the source is still, the formula is f' = f · (v ± vo) / v, with + for an observer moving toward the source and − for one moving away.
Worked example: an ambulance siren
An ambulance siren emits a steady 700 Hz tone and drives at 30 m/s. The speed of sound is 343 m/s.
Approaching the observer (use v − vs):
f' = 700 × 343 / (343 − 30) = 240 100 / 313 ≈ 767 Hz
Moving away from the observer (use v + vs):
f' = 700 × 343 / (343 + 30) = 240 100 / 373 ≈ 644 Hz
The same siren is heard about 123 Hz higher on the way in and about 56 Hz lower on the way out. That gap is the Doppler shift you hear as the car passes.
Red shift and blue shift
Light is a wave too, so the same effect applies. When a light source moves away from us, its light shifts toward the red end of the spectrum (a lower frequency). This is red shift. When it moves toward us, the light shifts toward blue (a higher frequency), which is blue shift.
Astronomers use red shift to show that most distant galaxies are moving away from us. The further away a galaxy is, the larger its red shift, and this is evidence that the universe is expanding.
What happens at the speed of sound?
As the source speeds up, the denominator v − vs gets smaller and the observed frequency climbs. When vs reaches v (Mach 1), the denominator is zero and the formula breaks down: the wave crests pile up into a single shock front. When a source moves faster than sound, the front behind it forms a cone, and a listener on the ground hears a sonic boom as the cone passes. The ratio vs / v is the Mach number.
Doppler effect examples in real life
- Radar speed guns send a radio or microwave pulse at a car. The frequency of the reflected pulse is shifted by the car's speed, so the gun can calculate it.
- Ultrasound scans measure the shift of high-frequency sound reflected from moving blood cells. Doctors use this to measure blood flow in arteries and the heart.
- Weather radar shows how fast rain and wind are moving toward or away from the radar.
- Astronomy uses red and blue shift to measure how fast stars and galaxies move.
Common mistakes
- Using the wrong sign. Toward the observer means the denominator is v − vs (higher pitch). Away means v + vs (lower pitch).
- Mixing up source and observer. The formula above assumes the source moves. If the listener moves, the speed goes in the numerator instead.
- Changing the wave speed. Moving the source changes the frequency and wavelength, not the speed of sound in the air.
- Forgetting units. Keep v and vs in m/s, or the frequency comes out wrong.
Frequently asked questions
What is the Doppler effect in simple words?
The Doppler effect is the change in pitch or colour you notice when something making a wave moves toward or away from you. A moving siren sounds higher as it approaches and lower as it leaves. The change happens because the wave crests get squashed together in front of the source and spread apart behind it.
What is the Doppler effect formula?
For a moving source and a still observer, the formula is f' = f · v / (v ± vs). Here f is the emitted frequency, v is the wave speed, and vs is the source speed. Use minus when the source moves toward the observer and plus when it moves away.
Does the Doppler effect change the speed of sound?
No. The speed of sound depends on the medium, such as 343 m/s in air at about 20 °C. The Doppler effect changes the frequency you hear and the wavelength between the source and the observer, but the wave still travels at the same speed through the air.
Why do stars show red shift?
Light from a star that is moving away from Earth has a lower frequency, so it shifts toward red. Astronomers measure this shift to find how fast the star or galaxy is receding. Most distant galaxies show red shift, which is evidence that the universe is expanding.
What is the difference between red shift and blue shift?
Red shift is a drop in light frequency when a source moves away from the observer. Blue shift is a rise in frequency when it moves toward the observer. Both come from the same Doppler effect, applied to light instead of sound.
Try it yourself
Open the Doppler effect simulation and set a source frequency of 700 Hz and a speed of 30 m/s. Watch the wave crests bunch up ahead of the source, then compare the frequency you hear when it approaches with the value from the formula above. Next, try a speed close to 343 m/s and see what happens to the crests. For the basics of wave speed and wavelength, read the parts of a wave or go to the Waves and Sound tool.
See it for yourself, in 3D and free.
Try it in the Doppler Effect