$A$ car $P$ approaching a crossing at a speed of $10 \, m/s$ sounds a horn of frequency $700 \, Hz$ when $40 \, m$ in front of the crossing. The speed of sound in air is $340 \, m/s$. Another car $Q$ is at rest on a road which is perpendicular to the road on which car $P$ is reaching the crossing. The driver of car $Q$ hears the sound of the horn of car $P$ when he is $30 \, m$ in front of the crossing. The apparent frequency heard by the driver of car $Q$ is ..... $Hz$.

$A$ whistle of frequency $540 Hz$ rotates in a horizontal circle of radius $2 m$ at an angular speed of $15 rad/s$. What is the highest frequency heard by a listener at rest with respect to the center of the circle (in $Hz$)? (Velocity of sound in air $= 330 m/s$)

$A$ 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 $= 330 \, m/s$).

$A$ car is moving towards a high cliff. The car driver sounds a horn of frequency $f$. The reflected sound heard by the driver has a frequency $2f$. If $v$ is the velocity of sound,then the velocity of the car,in the same velocity units,will be:

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 $ms^{-1}$)?