Question

Figure 9.4 shows a transmitter and receiver of waves contained in a single instrument. It is used to measure the speed V of a target object (idealized as a flat plate) that is moving directly toward the unit, by analyzing the waves reflected from it. (a) Apply Doppler equations twice, first with the target as observer and then with the target as a source, and show that the frequency fr of the reflected waves at the receiver is related to their source frequency f_s by

where v is the speed of the waves. (b) In many practical situations, V << v, show that, then the above equation becomes

Answer 1

(a) The frequency as received by the target (as observer) is

With the target as the source, the frequency received by the receiver is