Question

A car traveling at 24.3 m/s honks its horn as it directly approaches the side of a large building. The horn produces a long sustained note of frequency f0 = 213 Hz. The sound is reflected off the building back to the car's driver. The sound wave from the original note and that reflected off the building combine to create a beat frequency. What is the beat frequency that the driver hears (which tells him that he had better hit the brakes!)? Assume the speed of sound in air is 342 m/s.

Answer 1

Calculate the Doppler-shifted frequency of the received echo, fr.
Let V be the car speed and a the speed of sound.

fr = fo*[(V+a)/(V-a)] = 1.153*fo = 246 Hz
Subtract fo from that for the beat frequency, 33 Hz