$A$ source and an observer are moving towards each other with a speed equal to $\frac{v}{2}$,where $v$ is the speed of sound. The source is emitting sound of frequency $n$. The frequency heard by the observer will be

The frequency changes by $10\%$ as a sound source approaches a stationary observer with constant speed $v_s$. What would be the percentage change in frequency as the source recedes from the observer with the same speed? (Given that $v_s < v$,where $v$ is the speed of sound in air)

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)

Two sources of sound of same frequency are placed at a distance of $100\,m$ from each other. An observer moving in between them hears $4$ beats per second. If the distance between the sound sources is increased to $400\,m$,then the number of beats heard by him will be:

An observer is standing $500 \,m$ away from a vertical hill. Starting between the observer and the hill, a police van sounding a siren of frequency $1000 \,Hz$ moves towards the hill with a uniform speed. If the frequency of the sound heard directly from the siren is $970 \,Hz$, the frequency of the sound heard after reflection from the hill (in $Hz$) is about, (velocity of sound $= 330 \,m/s$):

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