An observer moves towards a stationary source of sound with a speed $\frac{1}{5}$th that of sound. The frequency of the sound emitted by the source is $f$. The apparent frequency recorded by the observer is

$A$ 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 $\,Hz$)

When an engine passes near a stationary observer,its apparent frequencies occur in the ratio $5/3$. If the velocity of sound is $340 \ m/s$,then the velocity of the engine is .... $m/s$.

$A$ stationary source of sound $A$ is producing sound of frequency $170 \, Hz$. Another source of sound $B$ producing sound of frequency $240 \, Hz$ is moving towards the source $A$ on a straight path with a uniform speed of $20 \, ms^{-1}$. An observer between $A$ and $B$ is moving towards the source $A$ along the straight path $BA$. If the number of beats heard by the observer is zero, the speed of the observer is . . . . . . $ms^{-1}$. (Speed of sound in air $= 340 \, ms^{-1}$).

When both source and listener are approaching each other,the observed frequency of sound is given by (where $V$ is the speed of sound,$V_L$ and $V_S$ are the velocities of the listener and source respectively,and $n_0$ is the radiated frequency):

When a car is approaching the observer,the frequency of the horn is $100 \, Hz$. After passing the observer,it is $50 \, Hz$. If the observer moves with the car,the frequency will be $\frac{x}{3} \, Hz$ where $x = .....$