Police RADAR

RADAR speed detectors bounce microwave radiation off of moving vehicles and detect the reflected waves. These waves are shifted in frequency by the Doppler effect, and the beat frequency between the directed and reflected waves provides a measure of the vehicle speed.

Speed detection calculation
Index

Traveling wave concepts
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Doppler Shift, Moving Target

The Doppler shift for relatively low velocity sources such as those encountered by police RADAR is given by

but in this case there are two shifts: one because the wave incident on the moving car is Doppler shifted and an additional shift because the reflection is from a moving object. The frequency shift of the reflected wave received at the source of the wave is

This shift is detected by measuring the beat frequency with the transmitted wave.

DerivationCalculation of wavelengthCalculation of frequencyDoppler effect for light
Index

Traveling wave concepts

Doppler concepts
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Beat Frequency and Speed

The beat frequency between a microwave transmitted signal and a reflected signal off a moving object is

where the target velocity is taken as positive if the target if approaching the transmitter. Police RADAR uses this method for measurement of auto speed.

Calculation of speed
Index

Traveling wave concepts

Doppler concepts
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Beat Frequency and Speed

For a transmitted frequency of GHz = Hz

the reflected frequency will be Hz

and the beat frequency will be Hz

if the speed of the vehicle is m/s = mi/hr = km/hr = ft/s

Note: If not entered as data, the transmitted frequency will default to 10.6 GHz, a typical X-band radar frequency. K-band units with frequencies on the order of 30 GHz are also used. Any parameters can be changed.
Police RADARExpressions used in calculationDoppler effect for electromagnetic waves
Index

Traveling wave concepts

Doppler concepts
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