The Doppler effect is the change in the observed frequency (or wavelength) of a wave when the source and the observer are moving relative to each other.
A common example is the sound of an ambulance siren:
- As the ambulance approaches you, the sound waves are compressed, so you hear a higher pitch.
- As it moves away, the sound waves are stretched out, so you hear a lower pitch.
The same principle applies not only to sound but also to light and radio waves.
How police radar guns use the Doppler effect
Police radar guns don't listen for sound—they transmit radio waves.
Here's how they work:
- The radar gun emits radio waves at a known frequency toward a vehicle.
- The waves bounce off the vehicle and return to the radar gun.
- If the vehicle is moving:
- Toward the radar gun, the reflected waves have a slightly higher frequency.
- Away from the radar gun, they have a slightly lower frequency.
- The radar gun measures this tiny frequency shift (the Doppler shift).
- Using the known properties of radio waves, it calculates the vehicle's speed.
Why the frequency changes twice
Unlike hearing a moving ambulance, radar waves experience the Doppler effect twice:
- First when the moving car "receives" the outgoing radio waves.
- Again when the moving car reflects those waves back to the stationary radar gun.
This double shift makes the frequency change larger and easier for the radar gun to measure accurately.
A simple example
Imagine a radar gun sends out a radio signal at 24.150 GHz.
- A parked car reflects it back at essentially the same frequency.
- A speeding car might return a signal that's only a few thousand hertz different—a tiny change compared with 24.150 billion hertz.
Even though the difference is extremely small, modern electronics can detect it very precisely and convert it into a speed such as 55 mph or 88 km/h.
Key idea
The Doppler effect doesn't measure distance—it measures how fast an object is moving toward or away from the radar gun (its radial speed). That's why the officer's position relative to the car's direction of travel matters: if the car isn't moving directly toward or away from the radar, the measured speed will be slightly lower than the car's true speed. This is known as the cosine effect.
