$A$ whistle of frequency $660 \,Hz$ moves in a circle of radius $1 \,m$ at an angular speed of $10 \,rad/s$. The highest frequency heard by a listener at a long distance and at rest with respect to the center of the circle is (Let speed of sound $= 340 \,m/s$.) (in $\,Hz$)

Two trains,one coming towards and another going away from an observer,both at $4 \; m/s$,produce a whistle simultaneously of frequency $300 \; Hz$. Find the number of beats produced. (Assume the speed of sound $v = 332 \; m/s$)

When a train approaches a stationary observer,the apparent frequency of the whistle is $n'$ and when the same train recedes away from the observer,the apparent frequency is $n''$. Then,the apparent frequency $n$ when the observer moves with the train is

Two men are walking along a horizontal straight line in the same direction. The man in front walks at a speed of $1.0 \,m \,s^{-1}$ and the man behind walks at a speed of $2.0 \,m \,s^{-1}$. $A$ third man is standing at a height of $12 \,m$ above the same horizontal line such that all three men are in a vertical plane. The two walking men are blowing identical whistles which emit a sound of frequency $1430 \,Hz$. The speed of sound in air is $330 \,m \,s^{-1}$. At the instant when the moving men are $10 \,m$ apart,the stationary man is equidistant from them. The frequency of beats in $Hz$ heard by the stationary man at this instant is:

Which pre-assumptions are used for the Doppler effect?

$A$ locomotive approaching a crossing at a speed of $20 \, m/s$ sounds a whistle of frequency $640 \, Hz$ when it is $1 \, km$ from the crossing. There is no wind and the speed of sound in air is $330 \, m/s$. What frequency is heard by an observer located $\sqrt{3} \, km$ away from the crossing on a straight road at a right angle to the locomotive's path (in $, Hz$)?