qies 42

Q.42 A source which is emitting sound of frequency f is initially at (– r, 0) and an observer is situated initially at (2r, 0). If observer and source both are moving with velocities  v observer = –  2 V i ^ - 2 V j ^  and  v source V 2 i ^ + V 2 j ^  , then which of the following is correct option ?
  (A) Apparent frequency first increases, then decreases and observer observes the original frequency once during the motion. 
(B) Apparent frequency first increases, them decreases and observer ​ observes the original frequency twice ​during the motion. 

(C) ​Apparent frequency first increases, them decreases during the motion and obsercver never obseerves the initial frequency.
(D) Apparent frequency continuously decreases and once during the motion. observer hears the original frequency.

Dear student
Apparent frequency will become equal to actual frequency when relative velocity between source and observer becomes perpendicular to the line joining the source and the observer.Motion of source with respect to observer is as shown in figure..As the source moves with respect to observer from point A to point B its component of velocity of source with respect to observer along the line joining them decreasesVelocity of source with respect to observer isVs,o=Vs-V0=(V2i^+V2j^)-(-2Vi^-2Vj)=(32Vi^+32Vj^)Angle made by this vector with X axis is θ so thattanθ=32V32V=1θ=45°As the source moves with respect to observer from point A to point B  component of velocity of source with respect to observer along the line joining them decreases as the value of θ increases from 45° to 90° so apparent frequency goes on decreasing till B .Relative  velocity of source with respect to observer along the line joining them becomes zero at point B.At this instant Apparent frequency will become equal to actual frequency .When source moves away from point B  velocity of source with respect to observer is  directed away from  the observer and it increases in magnitude so again apparent frequency goes on decreasingCorrect option is  fourth one.Regards

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