$A$ policeman on duty detects a drop of $10 \%$ in the pitch of the horn of a moving car as it crosses him. If the velocity of sound is $330 \, m/s$,calculate the speed of the car in $m/s$.

$A$ motor-cyclist moving towards a huge cliff with a speed of $18 \ kmh^{-1}$,blows a horn of source frequency $325 \ Hz$. If the speed of the sound in air is $330 \ ms^{-1}$,the number of beats heard by him is

$A$ whistle revolves in a circle with an angular speed of $20 \; rad/s$ using a string of length $50 \; cm.$ If the frequency of sound from the whistle is $385 \; Hz,$ then what is the minimum frequency heard by an observer,who is far away from the centre in the same plane? $(v = 340 \; m/s)$

$A$ train approaching a railway crossing at a speed of $120 \ km/h$ sounds a whistle of frequency $576 \ Hz$,when it is $288 \ m$ away from the crossing. The frequency heard by an observer standing on the road perpendicular to the track at a distance of $384 \ m$ from the crossing is (Speed of sound in air $= 340 \ m/s$): (in $Hz$)

When a car is approaching the observer,the frequency of the horn is $100 \, Hz$. After passing the observer,it is $50 \, Hz$. If the observer moves with the car,the frequency will be $\frac{x}{3} \, Hz$ where $x = .....$

$A$ man is watching two trains,one leaving and the other coming with an equal speed of $4\,m/s$. If they sound their whistles each of frequency $240\,Hz$,the number of beats per second heard by the man will be equal to: (velocity of sound in air $= 320\,m/s$)