It is possible to construct a device for determining the speed of moving objects using sonar. The device consists of a sound emitter and a detector. The emitter creates a sound of a single frequency. The outgoing sound reflects from a moving target and is Doppler shifted. When the incoming signal arrives at the detector, the incoming signal and outgoing signal are combined, so that the detector actually detects the beat between them. The detector is a square-amplitude detector, which is thus able to pick up the beat (see figures below).
In one experiment with the device, the emitter created an outgoing signal of 80 kHz, which was reflected from a vehicle. The received signal was 70 kHz. The two graphs above were obtained. The top figure shows the output of the detector in terms of power versus time. The bottom figure shows power as a function of frequency (Fourier analyzed function of the top figure above).
For these questions, use 343m/s for the speed of sound.
At time t = t0 (in the top figure above), the incoming and outgoing waves are