An observer standing at a station observes a frequency of $219 \, Hz$ when a train approaches and $184 \, Hz$ when the train goes away from him. If the velocity of sound in air is $340 \, m/s$,then the velocity of the train and the actual frequency of the whistle will be:

The frequency of a car horn changes from $400\, Hz$ to $500\, Hz$ as the car approaches a vertical wall. If the speed of sound is $330\, m/s$,then the speed of the car is $.....\, km/h$.

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 is moving with a velocity of $50 \ m/s$ towards a stationary observer. The observer measures the frequency of sound as $500 \ Hz$. The apparent frequency of sound as heard by the observer when the source is moving away from him with the same speed is (Speed of sound at room temperature $350 \ m/s$). (in $Hz$)

An observer moves towards a stationary source of sound with a speed $\frac{1}{5}$th that of sound. The frequency of the sound emitted by the source is $f$. The apparent frequency recorded by the observer is

$A$ source of sound of frequency $256 \ Hz$ is moving rapidly towards a wall with a velocity of $5 \ m/s$. The speed of sound is $330 \ m/s$. If the observer is between the wall and the source,then the number of beats per second heard will be .... $Hz$.