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JEE Advanced 2016 Paper 1

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Question : 13

Total: 54

Two loudspeakers M and N are located 20 m apart and emit sound at frequencies 118 Hz and 121 Hz, respectively. A car is initially at a point P, 1800 m away from the midpoint Q of the line MN and moves towards Q constantly at 60 km/hr along the perpendicular bisector of MN. It crosses Q and eventually reaches a point R, 1800 m away from Q. Let v(t) represent the beat frequency measured by a person sitting in the car at time t. Let vP,vQ and vR be the beat frequencies measured at locations P, Q and R, respectively. The speed of sound in air is 330ms−1.Which of the following statement(s) is(are) true regarding the sound heard by the person ?

The plot below represents schematically the variation of beat frequency with time
The plot below represents schematically the variations of beat frequency with time
The rate of change in beat frequency is maximum when the car passes through Q
vP+vR=2vQ

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