A traffic-control radar unit emits continuous microwaves at a rest frequency of 24.150 GHz toward an oncoming car on a straight, level road. The microwaves reflect from the car’s metal surfaces and return to the radar receiver. At the instant shown, the car moves directly toward the radar unit at 30.0 m/s. Assume the speed of light in air is 3.00×108m/s and that relativistic effects beyond the classical Doppler shift are negligible at this speed.
(a) Determine the frequency of the microwaves incident upon the car, as measured in the reference frame of the car.
(b) The car reflects the incident waves as though from a moving mirror. Determine the frequency of the waves that return to the radar receiver after reflection.
(c) The radar unit mixes the received signal with a portion of the original emitted signal, producing a beat frequency that digital electronics interpret to compute the car’s speed. Calculate this beat frequency. Express your answer to the nearest hertz.
(d) Suppose the same radar unit instead monitors a car receding at 30.0 m/s. Predict qualitatively whether the beat frequency magnitude increases, decreases, or remains unchanged compared with part (c), and justify your prediction without additional numerical calculation.