$A$ train sounding a whistle of frequency $510 \,Hz$ approaches a station at $72 \,km/hr$. The frequency of the note heard by an observer on the platform as the train $(1)$ approaches the station and then $(2)$ recedes from the station are respectively (in hertz) (velocity of sound in air $= 320 \,m/s$).

Two cars $X$ and $Y$ are approaching each other with velocities $36 \; km/h$ and $72 \; km/h$ respectively. The frequency of a whistle sound emitted by a passenger in car $X$,heard by the passenger in car $Y$,is $1320 \; Hz$. If the velocity of sound in air is $340 \; m/s$,the actual frequency of the whistle sound produced is ........ $Hz$.

The driver of a bus approaching a big wall notices that the frequency of his bus's horn changes from $420\, Hz$ to $490\, Hz$,when he hears it after it gets reflected from the wall. Find the speed of the bus (in $kmh^{-1}$) if the speed of sound is $330\, ms^{-1}$.

$A$ boy is walking away from a wall towards an observer at a speed of $1\, m/s$ and blows a whistle whose frequency is $680\, Hz$. The number of beats heard by the observer per second is (Velocity of sound in air $= 340\, m/s$).

Consider the Doppler effect in two cases. In the first case,an observer moves towards a stationary source of sound with a speed of $50 \,m/s$. In the second case,the observer is at rest and the source moves towards the observer with the same speed of $50 \,m/s$. Then the frequency heard by the observer will be [velocity of sound in air $= 330 \,m/s$.]

$A$ source of sound of frequency $640 \,Hz$ is moving at a velocity of $\frac{100}{3} \,m/s$ along a road, and is at an instant $30 \,m$ away from a point $A$ on the road. $A$ person standing at $O$, $40 \,m$ away from the road, hears sound of apparent frequency $v^{\prime}$. The value of $v^{\prime}$ is (velocity of sound $= 340 \,m/s$): (in $\,Hz$)