$A$ man is standing on a railway platform listening to the whistle of an engine that passes the man at a constant speed without stopping. If the engine passes the man at time $t_0$,how does the frequency $f$ of the whistle as heard by the man change with time?

An engine is moving with uniform speed along a circular track emitting a sound of frequency $400\, Hz$ as shown in the figure. The speed of the engine is $30\, m/s$ and the speed of sound is $330\, m/s$. An observer is standing inside the track. The maximum frequency observed by the observer is

$A$ highway truck has two horns $A$ and $B$. When sounded together, the driver records $50$ beats in $10$ seconds. With horn $B$ blowing and the truck moving towards a wall at a speed of $10 \,m/s$, the driver notices a beat frequency of $5 \,Hz$ with the echo. When the frequency of $A$ is decreased, the beat frequency with the two horns sounded together increases. Calculate the frequency of horn $A$. (Speed of sound in air $= 330 \,m/s$) (in $\,Hz$)

Two trains move towards each other with the same speed. The speed of sound is $340 \; m/s$. If the pitch of the whistle of one train heard by an observer on the other train changes by a factor of $9/8$,then the speed of each train is ........... $m/s$.

$A$ train is moving on a straight track with speed $20 \ ms^{-1}$. It is blowing its whistle at a frequency of $1000 \ Hz$. The percentage change in the frequency heard by a person standing near the track as the train passes him is (speed of sound $= 320 \ ms^{-1}$) close to .... $\%$

$A$ locomotive approaching a crossing at a speed of $20 \, m/s$ sounds a whistle of frequency $640 \, Hz$ when it is $1 \, km$ from the crossing. There is no wind and the speed of sound in air is $330 \, m/s$. What frequency is heard by an observer located $\sqrt{3} \, km$ away from the crossing on a straight road at a right angle to the locomotive's path (in $, Hz$)?