Two submarines are underwater and approaching each other head-on. Sub A has a sp

Question

Two submarines are underwater and approaching each other head-on. Sub A has a speed of 13m/s and sub B has a speed of 4 m/s. Sub A sends out a 1250Hz sonar wave that travels at a speed of 1522 m/s.
(Hints given are-4a) Include both motion of emitter [sub A]and motion of observer [sub B] effects. Always use each speedrelative to the medium of the wave. Here, as they are given [i.e.relative to the water].
4b) HINT: The reflected wave has the same frequency that sub Bdetects in part a) but now sub B acts as the emitter and sub A isthe observer.)

(a) What is the frequency of the sound detected by subB?
-----------Hz
(b) Part of the sonar wave is reflected from B and returns to A.What frequency does A detect for this reflected wave?
---------- Hz

Two submarines are underwater and approaching each other head-on. Sub A has a speed of 13m/s and sub B has a speed of 4 m/s. Sub A sends out a 1250Hz sonar wave that travels at a speed of 1522 m/s.
(Hints given are-4a) Include both motion of emitter [sub A]and motion of observer [sub B] effects. Always use each speedrelative to the medium of the wave. Here, as they are given [i.e.relative to the water].
4b) HINT: The reflected wave has the same frequency that sub Bdetects in part a) but now sub B acts as the emitter and sub A isthe observer.)

Explanation / Answer

vA = 13 m/s, vB =4 m/s. fs = 1250 Hz, u = 1522 m/s.

(a) What is the frequency of the sound detected by sub B?
fB = fs*(u + vB)/(u -vA) = 1264 Hz

(b) Part of the sonar wave is reflected from B and returns to A.What frequency does A detect for this reflected wave?
fA' = fB*(u + vA)/(u -vB) = 1278 Hz

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