An observer starts moving with uniform acceleration $a$ toward a stationary sound source emitting a whistle of frequency $n$. As the observer approaches the source,the apparent frequency $n'$ heard by the observer varies with time $t$ as:

$A$ 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?

$A$ sound source is tied to one end of a string of length $50 \ cm$ and is rotated with an angular speed of $40 \ rad \ s^{-1}$ in a horizontal plane. The ratio of the maximum and minimum frequencies of the sound heard by an observer standing at a distance of $10 \ m$ from the fixed end of the string is (speed of sound in air $= 340 \ m \ s^{-1}$).

$A$ car $P$ travelling at $20\,ms^{-1}$ sounds its horn at a frequency of $400\,Hz$. Another car $Q$ is travelling behind the first car in the same direction with a velocity $40\,ms^{-1}$. The frequency heard by the passenger of the car $Q$ is approximately $.......\,Hz$. [Take,velocity of sound $= 360\,ms^{-1}$]

$A$ bus driving along at $39.6 \,km/h$ is approaching a person who is standing at the bus stop,while honking repeatedly at an interval of $30 \,s$. If the speed of sound is $330 \,ms^{-1}$,at what interval will the person hear the horn?

The apparent frequency of a sound wave as heard by an observer is $10\%$ more than the actual frequency. If the velocity of sound in air is $330 \, m/s$,then
$(i)$ The source may be moving towards the observer with a velocity of $30 \, m/s$
$(ii)$ The source may be moving towards the observer with a velocity of $33 \, m/s$
$(iii)$ The observer may be moving towards the source with a velocity of $30 \, m/s$
$(iv)$ The observer may be moving towards the source with a velocity of $33 \, m/s$