An observer is standing $500 \,m$ away from a vertical hill. Starting between the observer and the hill, a police van sounding a siren of frequency $1000 \,Hz$ moves towards the hill with a uniform speed. If the frequency of the sound heard directly from the siren is $970 \,Hz$, the frequency of the sound heard after reflection from the hill (in $Hz$) is about, (velocity of sound $= 330 \,m/s$):

$A$ whistle revolves in a circle with an angular speed of $20 \; rad/s$ using a string of length $50 \; cm.$ If the frequency of sound from the whistle is $385 \; Hz,$ then what is the minimum frequency heard by an observer,who is far away from the centre in the same plane? $(v = 340 \; m/s)$

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 $S$ in the form of a block kept on a smooth horizontal surface is connected to a spring, as shown in the figure. If the spring oscillates with an amplitude of $50 \,cm$ along the horizontal between the wall and the observer $O$, the maximum frequency heard by the observer is $12.5 \%$ more than the minimum frequency heard by him. If the mass of the source of sound is $100 \,g$, the force constant of the spring is (Speed of sound in air is $340 \,ms^{-1}$) (in $\,N m^{-1}$)

$A$ stationary source is emitting sound at a fixed frequency $f_0$,which is reflected by two cars approaching the source. The difference between the frequencies of sound reflected from the cars is $1.2 \%$ of $f_0$. What is the difference in the speeds of the cars (in $km/h$) to the nearest integer? The cars are moving at constant speeds much smaller than the speed of sound,which is $330 \ m/s$.

The apparent frequency of a note,when a listener moves towards a stationary source with a velocity of $40 \ m/s$,is $200 \ Hz$. When the listener moves away from the same source with the same speed,the apparent frequency of the same note is $160 \ Hz$. The velocity of sound in air is (in $m/s$):