Two cars are moving on two perpendicular roads towards a crossing with uniform speeds of $72\; km/hr$ and $36\; km/hr$. If the first car blows a horn of frequency $280\; Hz$,then the frequency of the horn heard by the driver of the second car when the line joining the cars makes a $45^o$ angle with the roads will be .... $Hz$.

Two whistles $A$ and $B$ produce notes of frequencies $660 \ Hz$ and $596 \ Hz$ respectively. There is a listener at the mid-point of the line joining them. Now,the whistle $B$ and the listener start moving with a speed of $30 \ m/s$ away from the whistle $A$. If the speed of sound is $330 \ m/s$,how many beats will be heard by the listener?

$A$ driver in a car,approaching a vertical wall,notices that the frequency of his car horn has changed from $440 \, Hz$ to $480 \, Hz$ when it gets reflected from the wall. If the speed of sound in air is $345 \, m/s,$ then the speed of the car is $....... \, km/hr$.

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 $3$.

$A$ train whistling at a constant frequency is moving towards a station at a constant speed $V_S$. The train goes past a stationary observer on the station. The frequency $n'$ of the sound as heard by the observer is plotted as a function of time $t$. Identify the expected curve.

$A$ train approaching a railway platform with a speed of $20 \ ms^{-1}$ starts blowing the whistle. The speed of sound in air is $340 \ ms^{-1}$. If the frequency of the emitted sound from the whistle is $640 \ Hz$, the frequency of sound to a person standing on the platform will appear to be: (in $Hz$)