Two loudspeakers M and N are located 20 m apart and emit sound at frequencies 118 Hz an 121 Hz , respectively. A car is initially at a point $\mathrm{P}, 1800 \mathrm{~m}$ away from the midpoint Q of the line MN and moves towards Q constantly at $60 \mathrm{~km} / \mathrm{hr}$ along the perpendicular bisector of MN. It crosses $Q$ and eventually reaches a point $R, 1800 \mathrm{~m}$ 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 $v_B$ be the beat frequencies measured at locations P, Q and R, respectively. The speed of sound in air is $330 \mathrm{~ms}^{-1}$. Which of the following statement(s) is (are) true regarding the sound heard by the person?
Select ALL correct options:
A
The plot below represents schematically the variation of beat frequency with time
B
The plot below represents schematically the variation of beat frequency with time
C
$v_p+v_R=2 v_0$
D
The rate of change in beat frequency is maximum when the car passes through Q
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