Question

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?

Answer 1

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