A highway patrol is parked at the roadside on the 405 and sends out an audio-signal at 4.5 kHz to measure your speed asyou are passing by at a constant velocity. The cop measures you from behind as you move away from the police car. He measures a frequency of 3.5 kHz coming back after the wave is reflected off your car.
a. How fast were you moving?
b. What is the frequency of the signal that you hear in your car?
c. The policeman tickets you for violating the 70 mi/hour speed limit. You object and argue that the measurement was hampered by the cold air temperature near the freezing point and thus the fact that the speed of sound was smaller (vsound = 330 m/s). Could this different sound velocity really explain the measured frequency if you were not exceeding the speed limit?