Two loudspeakers $M$ and $N$ are located $20 \mathrm{~m}$ apart and emit sound at frequencies $118 \mathrm{~Hz}$ and $121 \mathrm{~Hz}$, respectively. $A$ car is initially at a point $P, 1800 \mathrm{~m}$ away from the midpoint $Q$ of the line $M N$ and moves towards $Q$ constantly at $60 \mathrm{~km} / \mathrm{hr}$ along the perpendicular bisector of $M N$. 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 tlie 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 $330 \mathrm{~m} \mathrm{~s}^{-1}$. Which of the following statement($s$) is(are) true regarding the sound heard by the person?
($A$) $v_P+v_R=2 v_Q$
($B$) 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
(image)
($D$) The plot below represents schematically the variation of beat frequency with time
(image)
IIT 2016, Advanced
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