$A$ railway engine whistling at a constant frequency moves with a constant speed. It goes past a stationary observer standing beside the railway track. The frequency $(n)$ of the sound heard by the observer is plotted against time $(t).$ Which of the following best represents the resulting curve?

$A$ man is standing between two trains moving away from and towards him,both with a speed of $4 \, m/s$. If both trains produce a sound of frequency $240 \, Hz$,calculate the number of beats heard by the man. (Speed of sound in air = $320 \, m/s$)

$A$ rocket is moving at a speed of $200\; m s^{-1}$ towards a stationary target. While moving, it emits a wave of frequency $1000\; Hz$. Some of the sound reaching the target gets reflected back to the rocket as an echo. Calculate:
$(1)$ the frequency of the sound as detected by the target and
$(2)$ the frequency of the echo as detected by the rocket.

$A$ toy-car,blowing its horn,is moving with a steady speed of $5\, m/s$,away from a wall. An observer,towards whom the toy car is moving,is able to hear $5\, beats$ per second. If the velocity of sound in air is $340\, m/s$,the frequency of the horn of the toy car is close to ... $Hz$

Two whistles $A$ and $B$ produce notes of frequencies $660 \ Hz$ and $596 \ Hz$ respectively. There is a listener at the mid-point of the line joining them. Now,the whistle $B$ and the listener start moving with a speed of $30 \ m/s$ away from the whistle $A$. If the speed of sound is $330 \ m/s$,how many beats will be heard by the listener?

$A$ bus moving with a uniform speed of $72 \,km/h$ towards a building blows a horn of frequency $1.7 \,kHz$. If the speed of sound in air is $340 \,m/s$, what will be the frequency of the echo heard by the bus driver (in $\,kHz$)?