# Submarine A detects sound from sub B. Find sub B's velocity.

Submarine A detects sound from sub B. Given the frequency received and knowing that emitted, find the velocity of sub B.

Submarine A, with velocity 21 m/sec, receives from directly behind it, the sound with frequency 266 cy/sec, from submarine B which is known to emit sound at 265 cy/sec.

The two submarines are 1800 meters apart. Speed of sound in sea water 1450 m/sec.

If the two subs maintain courses and speeds, will there be a collision, and if so, in how many seconds?

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#### Solution Preview

Recall that the Doppler equation is:

(1) f' = f (v + vs) / (v - vo) in which:

f = frequency emitted by source

f' = frequency received by observer

v = velocity of sound

vo = velocity of observer (+ if toward source, - if away from source)

vs = ...

#### Solution Summary

The expert finds the velocity of a submarine. The frequency and speed of the collisions are given. With good explanations and four separate steps, the problem is solved.