$A$ train is moving with a constant speed along a large circular track. The engine of the train emits a sound of frequency $f$. What is the frequency heard by the guard at the rear end of the train?

$A$ 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 $340\; m s^{-1}$.

$A$ source of sound is moving with a constant velocity of $20\, m/s$ emitting a note of frequency $1000\, Hz.$ The ratio of frequencies observed by a stationary observer while the source is approaching him and after it crosses him will be (Speed of sound $v = 340\, m/s$).

$A$ 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 = $320 \, m/s$)

When the observer moves towards a stationary source with velocity $V_{1}$,the apparent frequency of the emitted note is $F_{1}$. When the observer moves away from the source with velocity $V_{1}$,the apparent frequency is $F_{2}$. If $V$ is the velocity of sound in air and $F_{1} / F_{2} = 2$,then $V / V_{1}$ is equal to:

$A$ 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 $\,Hz$)