$A$ car moving towards a cliff emits sound of frequency '$n$'. If the difference in frequencies of the horn and its echo heard by the driver of the car is $10 \%$ of '$n$',then the speed of the car is nearly (Speed of sound in air is $336 \ m/s$) (in $m/s$)

$A$ student holds a tuning fork oscillating at $170 \,Hz$. He walks towards a wall at a constant speed of $2 \,ms^{-1}$. The beat frequency observed by the student between the tuning fork and its echo is (Velocity of sound $=340 \,ms^{-1}$ ) (in $\,Hz$)

When a car is approaching the observer,the frequency of the horn is $100 \, Hz$. After passing the observer,it is $50 \, Hz$. If the observer moves with the car,the frequency will be $\frac{x}{3} \, Hz$ where $x = .....$

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 $60 \ km/h$ 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 $330 \ m/s$. 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 (Left plot)
$(D)$ The plot below represents schematically the variation of beat frequency with time (Right plot)

The observer is moving with velocity $v_0$ towards the stationary source of sound and then after crossing moves away from the source with velocity $v_0$. Assume that the medium through which the sound waves travel is at rest. If $v$ is the velocity of sound and $n$ is the frequency emitted by the source,then the difference between apparent frequencies heard by the observer is:

$A$ source and an observer approach each other with the same velocity $50 \, m/s$. If the apparent frequency is $435 \, s^{-1}$,then the real frequency is .... $s^{-1}$ (Take speed of sound $v = 332 \, m/s$)