$A$ police van,moving at $22 \, m/s$,chases a motorcyclist. The policeman sounds a horn at $176 \, Hz$,while both of them move towards a stationary siren of frequency $165 \, Hz$ as shown in the figure. If the motorcyclist does not observe any beats,his speed must be .... $m/s$ (take the speed of sound $= 330 \, m/s$).

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:

Two sources $A$ and $B$ are sending notes of frequency $680 \ Hz$. $A$ listener moves from $A$ towards $B$ with a constant velocity $u$. If the speed of sound in air is $340 \ ms^{-1}$, what must be the value of $u$ so that he hears $10$ beats per second (in $ms^{-1}$)?

$A$ siren emitting sound of frequency $800 \; Hz$ is going away from a static listener with a speed of $30 \; m/s$. The frequency of the sound heard by the listener is... $Hz$ (take velocity of sound as $330 \; m/s$).

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:

$A$ man is standing on a railway platform listening to the whistle of an engine that passes the man at a constant speed without stopping. If the engine passes the man at time $t_0$,how does the frequency $f$ of the whistle as heard by the man change with time?