$A$ 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 with a frequency of $90 \, \text{vibrations/sec}$ moves towards a stationary observer with a velocity of $1/10 \, V$, where $V$ is the speed of sound. What frequency will the observer hear in $\text{vibrations/sec}$?

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 $ms^{-1}$)?

Two trains $A$ and $B$ are moving with speeds $20 \ m/s$ and $30 \ m/s$ respectively in the same direction on the same straight track,with $B$ ahead of $A$. The engines are at the front ends. The engine of train $A$ blows a long whistle. Assume that the sound of the whistle is composed of components varying in frequency from $f_1=800 \ Hz$ to $f_2=1120 \ Hz$,as shown in the figure. The spread in the frequency (highest frequency - lowest frequency) is thus $320 \ Hz$. The speed of sound in still air is $340 \ m/s$.
$1.$ The speed of sound of the whistle is
$(A)$ $340 \ m/s$ for passengers in $A$ and $310 \ m/s$ for passengers in $B$
$(B)$ $360 \ m/s$ for passengers in $A$ and $310 \ m/s$ for passengers in $B$
$(C)$ $310 \ m/s$ for passengers in $A$ and $360 \ m/s$ for passengers in $B$
$(D)$ $340 \ m/s$ for passengers in both the trains
$2.$ The distribution of the sound intensity of the whistle as observed by the passengers in train $A$ is best represented by
$3.$ The spread of frequency as observed by the passengers in train $B$ is
$(A)$ $310 \ Hz$ $(B)$ $330 \ Hz$ $(C)$ $350 \ Hz$ $(D)$ $290 \ Hz$
Give the answer for question $1, 2$ and $3$.

$A$ 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 $320\, m/s$)

An observer moves towards a stationary source of sound,with a velocity one-fifth of the velocity of sound. What is the percentage increase in the apparent frequency (in $\%$)?