Question

A police car moving at 13.0 m/s follows a speeding car moving at 23.0 m/s. A radar unit in the police car emits a 3.50 × 1010 Hz signal, which is reflected by the other car. What is the change between the emitted frequency and the frequency of the reflected signal detected by the radar unit? (Enter a negative value if the emitted frequency is greater than the reflected frequency.)

Answer 1

By dopplers formula,

frequency observed by speeding car, f1 = f0*(V - Vs)/(V- Vp)

frequency observed by police car after reflection, f2 = f1*(V+Vp)/(V+Vs)

= f0*(V - Vs)/(V- Vp) *(V+Vp)/(V+Vs)

= 3.5e10 *(343-23)/(343-13) *(343+13)/(343+23)

= 3.30*10^10 Hz

change in frequency = f2 - f0 = -2*10^-9 Hz