$A$ $SONAR$ system fixed in a submarine operates at a frequency of $40.0 \; kHz$. An enemy submarine moves towards the $SONAR$ with a speed of $360 \; km/h$. What is the frequency (in $kHz$) of sound reflected by the submarine (in $; kHz$)? Take the speed of sound in water to be $1450 \; m/s$.

Two men are walking along a horizontal straight line in the same direction. The man in front walks at a speed $1.0 \ m \ s^{-1}$ and the man behind walks at a speed $2.0 \ m \ s^{-1}$. $A$ third man is standing at a height $12 \ m$ above the same horizontal line such that all three men are in a vertical plane. The two walking men are blowing identical whistles which emit a sound of frequency $1430 \ Hz$. The speed of sound in air is $330 \ m \ s^{-1}$. At the instant when the moving men are $10 \ m$ apart,the stationary man is equidistant from them. The frequency of beats in $Hz$ heard by the stationary man at this instant is:

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 $3$.

$A$ source of sound $S$ emitting waves of frequency $100 \, Hz$ and an observer $O$ are located at some distance from each other. The source is moving with a speed of $19.4 \, m s^{-1}$ at an angle of $60^{\circ}$ with the source-observer line as shown in the figure. The observer is at rest. The apparent frequency observed by the observer is .... $Hz$ (velocity of sound in air $330 \, m s^{-1}$).

$A$ car is moving with a speed of $72 \text{ km/h}$ towards a roadside source that emits sound at a frequency of $850 \text{ Hz}$. The car driver listens to the sound while approaching the source and again while moving away from the source after crossing it. If the velocity of sound is $340 \text{ m/s}$, the difference of the two frequencies the driver hears is: (in $\text{ Hz}$)

$A$ car is moving towards a high cliff. The car driver sounds a horn of frequency $f$. The reflected sound heard by the driver has a frequency $2f$. If $v$ is the velocity of sound,then the velocity of the car,in the same velocity units,will be: