$A$ table is revolving on its axis at $5$ revolutions per second. $A$ sound source of frequency $1000 \text{ Hz}$ is fixed on the table at $70 \text{ cm}$ from the axis. The minimum frequency heard by a listener standing at a distance from the table will be .... $\text{ Hz}$ (speed of sound $= 352 \text{ m/s}$)

$A$ train,standing at the outer signal of a railway station,blows a whistle of frequency $400\; Hz$ in still air.
$(i)$ What is the frequency of the whistle for a platform observer when the train $(a)$ approaches the platform with a speed of $10\; m s^{-1}$,$(b)$ recedes from the platform with a speed of $10\; m s^{-1}$?
$(ii)$ What is the speed of sound in each case? The speed of sound in still air can be taken as $340\; m s^{-1}$.

$A$ boy standing on a platform observes the frequency of a train horn as it passes by. The change in the frequency noticed as the train approaches and recedes him with a velocity of $108 \text{ km/h}$ is (speed of sound in air $= 330 \text{ m/s}$) (in $\%$)

$A$ bus driving along at $39.6 \,km/h$ is approaching a person who is standing at the bus stop,while honking repeatedly at an interval of $30 \,s$. If the speed of sound is $330 \,ms^{-1}$,at what interval will the person hear the horn?

$A$ source of sound is travelling with a velocity of $40 \, km/h$ towards an observer and emits sound of frequency $2000 \, Hz$. If the velocity of sound is $1220 \, km/h$,what is the apparent frequency heard by the observer in $Hz$?

Two sources $A$ and $B$ are sounding notes of frequency $660 \, Hz$. $A$ listener moves from $A$ to $B$ with a constant velocity $u$. If the speed of sound is $330 \, m/s$,what must be the value of $u$ so that he hears $8$ beats per second?