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I am confused about this problem. I know it involves the Doppler effect but i dont know what to do. Thanks for any help.

A submarine with a cruising speed of 15.0 m/s uses a sonar (Sound Navigation and Ranging) device
operating at 15000 Hz. The speed of sound in sea water at the submarine's depth is 1551 m/s.
Calculate the frequency of the echo a sonar operator would receive from a torpedo coming directly
towards the submarine at a speed of 30.0 m/s.

Hello Jimmy,

Both objects are moving in the medium, so the formula needs to consider V, Vo, and Vs. If the torpedo sensed incoming frequencies, this is the formula that would yield the frequency, f', the torpedo, as observer, would detect:
f' = f*(V + Vo)/(V - Vs)
where f = 15,000 Hz, V = 1551 m/s, Vo = 30.0 m/s, and Vs = 15 m/s.

The same principle can be used again to find the frequency observed by the sub. However the wave reflected back from the torpedo will appear the same as if the torpedo had emitted the frequency f', so now the formula should be written
f'' = f'*(V + Vo)/(V - Vs)
Note that now the observer is the submarine.

I hope this helps,


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Steve Johnson


I would be delighted to help with questions up through the first year of college Physics. Particularly Electricity, Electronics and Newtonian Mechanics (motion, acceleration etc.). I decline questions on relativity and Atomic Physics. I also could discuss the Space Shuttle and space flight in general.


I have a BS in Physics and an MS in Electrical Engineering. I am retired now. My professional career was in Electrical Engineering with considerable time spent working with accelerometers, gyroscopes and flight dynamics (Physics related topics) while working on the Space Shuttle. I gave formal classroom lessons to technical co-workers periodically over a several year period.

BS Physics, North Dakota State University
MS Electrical Engineering, North Dakota State University

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