A French submarine and a U.S. submarine move toward each other during maneuvers

Question

A French submarine and a U.S. submarine move toward each other during maneuvers in motionless water in the North Atlantic (see the figure). The French sub moves at speed vF , and the U.S. sub at speed vUS. The French sub sends out a sonar signal (sound wave in water) at frequency f. Sonar waves travel at speed v. (a) What is the signal's frequency as detected by the U.S. sub? (b) What frequency is detected by the French sub in the signal reflected back to it by the U.S. sub? State your answers in terms of the given variables.

A French submarine and a U.S. submarine move toward each other during maneuvers in motionless water in the North Atlantic (see the figure). The French sub moves at speed vF , and the U.S. sub at speed vUS. The French sub sends out a sonar signal (sound wave in water) at frequency f. Sonar waves travel at speed v. (a) What is the signal's frequency as detected by the U.S. sub? (b) What frequency is detected by the French sub in the signal reflected back to it by the U.S. sub? State your answers in terms of the given variables.

Explanation / Answer

fus=(V+Vus/V-Vf)*f
The US sub is now the source emitting frequency fus and the French sub is the detector which observes frequency fobs
fobs=(V+Vf/V-Vus)*fus

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