$A$ boy is walking away from a wall towards an observer at a speed of $1\, m/s$ and blows a whistle whose frequency is $680\, Hz$. The number of beats heard by the observer per second is (Velocity of sound in air $= 340\, m/s$).

Two sources $A$ and $B$ are sending notes of frequency $680 \ Hz$. $A$ listener moves from $A$ towards $B$ with a constant velocity $u$. If the speed of sound in air is $340 \ ms^{-1}$, what must be the value of $u$ so that he hears $10$ beats per second (in $ms^{-1}$)?

When an engine passes near a stationary observer,its apparent frequencies occur in the ratio $5/3$. If the velocity of sound is $340 \ m/s$,then the velocity of the engine is .... $m/s$.

An observer is standing $500 \,m$ away from a vertical hill. Starting between the observer and the hill, a police van sounding a siren of frequency $1000 \,Hz$ moves towards the hill with a uniform speed. If the frequency of the sound heard directly from the siren is $970 \,Hz$, the frequency of the sound heard after reflection from the hill (in $Hz$) is about, (velocity of sound $= 330 \,m/s$):

Which of the following statements is false?

$A$ train blowing its whistle moves with constant speed on a straight track towards an observer and then crosses him. If the ratio of the difference between the actual and apparent frequencies is $3:2$ in the two cases (approaching and receding),then the speed of the train is (where $v$ is the speed of sound).