(III) A radar “speed gun” emits microwaves of frequency f0 = 36.0 GHz. When the gun is pointed at an object moving toward it at speed v, the object senses the microwaves at the Doppler-shifted frequency f. The moving object reflects these microwaves at this same frequency f. The stationary radar apparatus detects these reflected waves at a Doppler-shifted frequency f′. The gun combines its emitted wave at f0 and its detected wave at f′. These waves interfere, creating a beat pattern whose beat frequency is fbeat = f′ − f0. (a) Show that
if
If the accuracy of the speed gun is to be 1 km/h, to what accuracy must the beat frequency be measured?
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