The engine of a train moving with speed $10\,ms^{-1}$ towards a platform sounds a whistle at frequency $400\,Hz$. The frequency heard by a passenger inside the train is $........\,Hz$ (neglect air speed. Speed of sound in air $330\,ms^{-1}$). (in $,Hz$)

An engine sounding a whistle of frequency $1152 \ Hz$ is receding from a stationary observer at $72 \ km/h$. If the velocity of sound in air is $340 \ m/s$,then the frequency of the note heard by the observer is: (in $Hz$)

An engine is moving with uniform speed along a circular track emitting a sound of frequency $400\, Hz$ as shown in the figure. The speed of the engine is $30\, m/s$ and the speed of sound is $330\, m/s$. An observer is standing inside the track. The maximum frequency observed by the observer is

$A$ train $S_1$,moving with a uniform velocity of $108 \ km/h$,approaches another train $S_2$ standing on a platform. An observer $O$ moves with a uniform velocity of $36 \ km/h$ towards $S_2$,as shown in the figure. Both the trains are blowing whistles of the same frequency $120 \ Hz$. When $O$ is $600 \ m$ away from $S_2$ and the distance between $S_1$ and $S_2$ is $800 \ m$,the number of beats heard by $O$ is: [Speed of sound $= 330 \ m/s$]

$A$ source of sound emits a sound wave of frequency '$f$' and moves towards an observer with a velocity $\frac{V}{3}$,where $V$ is the velocity of sound. If the observer moves away from the source with a velocity $\frac{V}{5}$,the apparent frequency heard by him will be:

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