$A$ whistle sends out $256$ waves in a second. If the whistle approaches the observer with a velocity equal to $\frac{1}{3}$ of the velocity of sound in air,calculate the number of waves per second the observer will receive.

An obstacle is moving towards the source with velocity $v$. The sound is reflected from the obstacle. If $c$ is the speed of sound and $\lambda$ is the wavelength,then the wavelength of the reflected wave $(\lambda_{r})$ is

$A$ source and an observer approach each other with the same velocity $50 \, m/s$. If the apparent frequency is $435 \, s^{-1}$,then the real frequency is .... $s^{-1}$ (Take speed of sound $v = 332 \, m/s$)

An observer is moving away from a source of sound of frequency $100 \, Hz$. His speed is $33 \, m/s$. If the speed of sound is $330 \, m/s$,then the observed frequency is .... $Hz$.

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 $3$.

$A$ sound wave of frequency $\nu$ travels horizontally to the right. It is reflected from a large vertical plane surface moving to the left with a speed $v$. The speed of sound in the medium is $c$. Then: