$A$ person observes two moving trains. Train $A$ is reaching the station and train $B$ is leaving the station, both with an equal speed of $30 \text{ m/s}$. If both trains emit sounds with a frequency of $300 \text{ Hz}$, and the speed of sound is $330 \text{ m/s}$, what is the difference in the frequencies heard by the person (in $\text{ Hz}$)?

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 .... $Hz$.

The engine of a train moving with speed $10\,ms^{-1}$ towards a platform sounds a whistle at frequency $400\,Hz$. The frequency heard by a passenger inside the train is $........\,Hz$ (neglect air speed. Speed of sound in air $330\,ms^{-1}$). (in $,Hz$)

An observer moves towards a stationary source of sound with a velocity of one-fifth of the velocity of sound. The percentage increase in the apparent frequency is (in $\%$)

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 $3$.

$A$ musician using an open flute of length $50\,cm$ produces second harmonic sound waves. $A$ person runs towards the musician from another end of a hall at a speed of $10\,km/h.$ If the wave speed is $330\,m/s,$ the frequency heard by the running person shall be close to...... $Hz$