The pitch of the whistle of an engine appears to drop by $20 \%$ of its original value when it passes a stationary observer. If the speed of sound in air is $350 \ m/s$,then the speed of the engine in $m/s$ is:

Two men are walking along a horizontal straight line in the same direction. The man in front walks at a speed $1.0 \ m \ s^{-1}$ and the man behind walks at a speed $2.0 \ m \ s^{-1}$. $A$ third man is standing at a height $12 \ m$ 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:

$A$ policeman blows a whistle of frequency $400 \ Hz$. $A$ car driver is approaching the policeman. The speed of the car is $54 \ km/h$. The change in frequency experienced by the driver,when the driver approaches the policeman and after he crosses the policeman,is ... $Hz$ [Velocity of sound is $350 \ m/s$]

$A$ 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 $\%$)

Obtain the equation of frequency observed by an observer for a moving source and a moving observer at different velocities.

$A$ source of sound emitting a note of frequency $200 Hz$ moves towards an observer with a velocity $v$ equal to the velocity of sound. If the observer also moves away from the source with the same velocity $v$,the apparent frequency heard by the observer is .... $Hz$