# Two loudspeakers M and N are located 20m apart and emit

Two loudspeakers M and N are located 20m 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 Let n(t) represent the beat frequency measured by a person sitting in the car at time t. Let n , n and n be the beat frequencies measured at locations P, Q and R, respectively. The speed of sound in air is 330 ms–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

**Answer: (a) The plot below represents schematically the variation of beat frequency with time, (c) The rate of change in beat frequency is maximum when the car passes through Q & (d) Vp + Vr = 2Vq**