You're cruising down the highway, and the radio's playing your favorite song. Your speedometer said sixty-five the last time you checked, but that was five minutes ago and your foot's been getting heavier on the accelerator ever since. Then you see the flash of red and blue lights in your rear-view mirror. What's that officer? Eighty miles per hour! How did you know?
You were probably caught with radar. A police radar gun shines a tight beam of microwave radiation, much the same way a flashlight shines a narrow beam of visible light. When the microwaves hit the front of an oncoming car, some of them are reflected back into the radar gun.
You can think of the microwave beam as a stream of evenly spaced ping pong balls. If these bounce against a stationary wall, the balls will return with the same amount of space between them as in the original stream. If the wall is moving toward you, each successive ball has less distance to go than the one in front of it. This will reduce the spacing between the returning balls. The faster the wall moves, the tighter the spacing between the returning balls.
For microwave radiation, this spacing translates as the wave's frequency. An oncoming car will bounce back a beam with a higher frequency than the original beam. By measuring exactly how much higher this return frequency is, a radar gun can compute your car's speed. Incidentally, by the time a radar gun targets your own car, it's already too late to reduce your speed.
A radar detector works by sensing the faint microwave signal that's scattered by other cars farther up the road. Of course radar detectors are illegal in many states. But then, so is speeding.