$A$ source emitting sound of frequency $288 \,Hz$ is tied to a string of $100 \,cm$ length and rotated with an angular velocity of $20 \,rad/s$ in the horizontal plane. The range of frequencies heard by an observer standing at a distance of $5 \,m$ from the source is (in $Hz$) (Speed of sound in air $= 340 \,m/s$)

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)

Obtain the equation of frequency observed by an observer for a moving source and a moving observer at different velocities.

$A$ source of sound whose frequency is $1000 \text{ Hz}$ is moving with a speed of $33 \text{ m/s}$. The waves reflected by a fixed obstacle are registered by a receiver that moves together with the source. If the speed of the sound waves is $330 \text{ m/s}$, then the frequency registered by the receiver is: (in $\text{ kHz}$)

An engine giving a whistle is moving towards a stationary observer with a speed of $110\, m/s$. What will be the ratio of the frequency of the whistle heard when the engine is approaching and receding from the observer? (Speed of sound $= 330\, m/s$)

$A$ car travelling at a speed of $54 \ km/h$ towards a wall sounds a horn of frequency $400 \ Hz$. The difference in the frequencies of two sounds,one received directly from the car and the other reflected from the wall,noticed by a person standing between the car and the wall is (speed of sound in air is $335 \ m/s$):