Question

A police officer uses a radar gun that emits electromagnetic waves with a frequency of 10.525 GHz (1.0525 1010 Hz). Assume the police officer is at rest, and is aiming the radar gun at vehicles traveling either directly toward, or directly away from, the radar gun. Assume the speed limit is 110 km/h, as it is on many Canadian highways. The police officer observes reflected waves that have a frequency of 2460 Hz below the frequency of the emitted waves.

Required:
a. At what speed is the car moving?
b. Choose the two correct statements about this situation.

1. The car is moving toward the police officer.
2. The car is moving away from the police officer.
3. The police officer should not cite the driver for speeding.
4. The police officer should cite the driver for speeding.

Answer 1

Step-by-step explanation:

For Doppler effect in radar the formula is as follows

Δf = f₀ x 2v /c

Δf is change in frequency in reflected wave , f₀ is original frequency , v is velocity of source and c is velocity of right .

Δf = 2460 Hz , f₀ = 1.0525 x 10¹⁰ Hz , v = ? c is velocity of light .

2460 = 1.0525 x 10¹⁰ x 2 v / 3 x 10⁸

2460 = 105.25 x 2 v / 3

v = 2460 x 3 / (105.25 x 2 )

v = 35 .06 m /s .

(b)

Since the observed frequency is less , the source is moving away from the observer .

option (2) is correct .