To catch speeders, a police radar gun detects the beat frequency between the signal it emits and that which reflects off a moving vehicle. What would be the beat frequency for an emitted signal of 900 Mhz reflected from a car moving at 30 m/s ?

Short Answer

Expert verified

The beat frequency between the Doppler shifted frequency and original frequency is180Hz .

Step by step solution

01

Write the given data from the question

The speed of the car,vs=30m/s

The frequency of the emitted signal, f=900Mhz

02

Beat frequency

The expression for the Doppler shift is given as follows.

ff=v5c

Here, v5 is the speed of the source, c is the speed of the light andf is the beat frequency.

03

Calculate the beat frequency for the emitted signal

To calculate the beat frequency, equation for beat frequency and Doppler shift required.

ff=2Vtargetc …… (i)

Calculate the beat frequency,

Substitute 3×108m/sforc,900MHzforfand30m/sforVsinto equation (i).

f900×106=2×303×108f=603×108×900×106f=5403f=180Hz

Hence the beat frequency between the Doppler shifted frequency and original frequency is 180 Hz .

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