$A$ passenger is sitting in a train which is moving fast. The engine of the train blows a whistle of frequency $n$. If the apparent frequency of sound heard by the passenger is $f$, then:

$A$ source,approaching with speed $u$ towards the open end of a stationary pipe of length $L$,is emitting a sound of frequency $f_s$. The farther end of the pipe is closed. The speed of sound in air is $v$ and $f_0$ is the fundamental frequency of the pipe. For which of the following combination$(s)$ of $u$ and $f_s$,will the sound reaching the pipe lead to a resonance?
$(A)$ $u=0.8 v$ and $f_s=f_0$
$(B)$ $u=0.8 v$ and $f_s=2 f_0$
$(C)$ $u=0.8 v$ and $f_s=0.5 f_0$
$(D)$ $u=0.5 v$ and $f_s=1.5 f_0$

$A$ source of sound is travelling at $\frac{100}{3} \, m/s$ along a road,towards a point $A$. When the source is $3 \, m$ away from $A$,a person is standing at a point $O$ on a road perpendicular to the path of the source. The distance of $O$ from $A$ at that time is $4 \, m$. If the original frequency is $640 \, Hz$,then the apparent frequency heard by the person is ...... $Hz$ (speed of sound is $340 \, m/s$).

$A$ train is moving with a uniform speed $33 \ m/s$ and an observer is approaching the train with the same speed. If the train blows a whistle of frequency $1000 \ Hz$ and the velocity of sound is $333 \ m/s$, then the apparent frequency of the sound that the observer hears is: (in $Hz$)

Two trains $A$ and $B$ are moving towards each other with speeds $72 \ km/h$ and $36 \ km/h$ respectively. The train $A$ whistles at $640 \ Hz$ frequency. Before the trains meet,the frequency of sound heard by a passenger in Train $B$ is (Speed of sound in air $= 340 \ m/s$). (in $Hz$)

When the listener 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 $\frac{F_1}{F_2} = 2$,then find the ratio $\frac{V}{V_1}$.