An observer moves towards a stationary source of sound with a speed $\frac{1}{5}^{\text{th}}$ of the speed of sound. The wavelength and frequency of the waves emitted by the source are $\lambda$ and $f$ respectively. The apparent frequency and wavelength heard by the observer are respectively,

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)

Consider two sound sources $S_1$ and $S_2$ having the same frequency $100\,Hz$ and the observer $O$ located between them as shown in the figure. All three are moving with the same velocity in the same direction. The beat frequency heard by the observer is .... $Hz$.

Two cars $A$ and $B$ are moving in the same direction with speeds $36 \, km/hr$ and $54 \, km/hr$ respectively. Car $B$ is ahead of $A$. If $A$ sounds a horn of frequency $1000 \, Hz$ and the speed of sound in air is $340 \, m/s$,the frequency of sound received by the driver of car $B$ is ..... $Hz$.

An engine sounding a whistle of frequency $1152 \ Hz$ is receding from a stationary observer at $72 \ km/h$. If the velocity of sound in air is $340 \ m/s$,then the frequency of the note heard by the observer is: (in $Hz$)

An observer and a source emitting sound of frequency $120 \,Hz$ are on the $X$-axis. The observer is stationary while the source of sound is in motion given by the equation $x=3 \sin \omega t$ (where $x$ is in metres and $t$ is in seconds). If the difference between the maximum and minimum frequencies of the sound observed by the observer is $22 \,Hz$,then the value of $\omega$ is (speed of sound in air $=330 \,ms^{-1}$):