Question

Police radars determine speed by measuring the Doppler shift of radio waves reflected by a moving vehicle. They do so by determining the beat frequency between the reflected wave and the 10.5 GHz emitted wave. Some units can be calibrated by using a tuning fork; holding a vibrating fork in front of the unit causes the display to register a speed corresponding to the vibration frequency. A tuning fork is labeled ""55 mph."" What is the frequency of the tuning fork?

Answer 1

Answer: 0.81 GHz

Explanation:As written in the question police radars works by determining the beat frequency between sent and reflected wave. This beat frequency is just difference of the frequencies of the sent and reflected wave.

To Calibrate the Radar the turning fork must produce the beat frequency similar to that produce by reflected wave at right speed which in this case is 55mph

Hence we know that turning fork frequency=Δf

Δf=f'-f

here f=10.5 Ghz

f=10.5 *10^9

f=10500000000

also

v_s=55mph

v_s=24.5872 m/s

since the source is moving a/c to doppler effect

$f'=f\frac{v}{v-v_s}$

taking speed of sound to be v=344m/s

$f'=10500000000*\frac{344}{344-24.5872}$

f'=11.3*10^9

Δf=8.08*10^8

Δf=0.81 GHz