$A$ person is observing two trains,one coming towards him and the other leaving with the same speed $4\, m/s$. If their whistling frequencies are $240\, Hz$ each,then the number of beats per second heard by the person will be: (if the velocity of sound is $320\, m/s$)

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:

Two cars are moving on two perpendicular roads towards a crossing with uniform speeds of $72\; km/hr$ and $36\; km/hr$. If the first car blows a horn of frequency $280\; Hz$,then the frequency of the horn heard by the driver of the second car when the line joining the cars makes a $45^o$ angle with the roads will be .... $Hz$.

When a train is approaching a stationary observer,the apparent frequency of the whistle of the train is $n_1$,and when the train is moving away from the observer,the apparent frequency is $n_2$. The frequency of the whistle noticed by the observer when he moves with the train is . . . . . . .

$A$ small source of sound vibrating at a frequency $500 Hz$ is rotated along a circle of radius $\frac{100}{\pi} cm$ at a constant angular speed of $5$ revolutions per second. The minimum and maximum frequency of the sound observed by a listener situated in the plane of the circle is (Speed of sound is $332 ms^{-1}$)

$A$ source and an observer move away from each other with the same velocity of $10 \,ms^{-1}$ with respect to the ground. If the observer finds the frequency of sound coming from the source as $1980 \,Hz$, then the actual frequency of the source is (speed of sound in air $= 340 \,ms^{-1}$). (in $\,Hz$)