Answer to Question #171326 in Electrical Engineering for Thelston

Question #171326

A microwave detector is being used to measure the velocity of a vehicle driving normally to the face of the detector. The microwave detector has the following properties and inputs: Frequency f0 = 24.15 GHz Doppler frequency shift = 50 Hz S = 0.5 mV/g How fast is the vehicle going in meters/sec?

Expert's answer

The Doppler effect is a change in the observed radiation frequency due to the movement of the source and/or the observer. The microwave detector uses electromagnetic radiation, the speed of which is equal to the speed of light, which means that the wavelength will be equal to

"\\lambda=\\frac c {f0}=\\frac {299792458 \\space m\/s}{24.15\\cdot10^9 \\space Hz}"

Formula for Doppler Radar Frequency Shift:

"\\Delta f=f-f0=f0(\\frac {c\\pm v}{c \\mp v})-f0"

The equation for a vehicle moving towards a stationary source (microwave detector) is as follows:

"\\Delta f=f0(\\frac {c+ v}{c})-f0=f0 \\frac v c=\\frac v \\lambda"

Vehicle speed:

"v=\\Delta f \\cdot \\lambda=\\frac {299792458 \\space m\/s}{24.15\\cdot10^9 \\space Hz}50Hz\\approxeq0.62 \\frac m s"

Answer: 0.62 meters/sec

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