Question

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 v_P, v_Q and v_R be the beat frequencies measured at locations P, Q and R, respectively. The speed of sound in air is 330 m s^-1 . Which of the following statement(s) is(are) true regarding the sound heard by the person? 

(A) v_P + v_R = 2v_Q 

(B) The rate of change in beat frequency is maximum when the car passes through Q 

(C) The plot below represents schematically the variation of beat frequency with time

(D) The plot below represents schematically the variation of beat frequency with time

Answer 1

(A) v_P + v_R = 2v_Q 

(B) The rate of change in beat frequency is maximum when the car passes through Q 

(C) The plot below represents schematically the variation of beat frequency with time

Now, sin θ =1 at Q (maximum) 

∴ rate of change in beat frequency is maximum at Q