The velocity of sound is $340 \,m/s$. $A$ source of sound having a frequency of $90 \,Hz$ is moving towards a stationary observer with a speed of one-tenth that of sound. The apparent frequency of sound as heard by the observer is: (in $\,Hz$)

Two whistles $A$ and $B$ each have a frequency of $500\,Hz$. $A$ is stationary and $B$ is moving towards the right (away from $A$) at a speed of $50\,m/s$. An observer is between the two whistles moving towards the right with a speed of $25\,m/s$. The velocity of sound in air is $350\,m/s$. Assume there is no wind. Then which of the following statements are true:

$A$ vibrating tuning fork is moving slowly and uniformly in a horizontal circular path of radius $8 \, m$. The shortest distance of an observer in the same plane from the tuning fork is $9 \, m$. The distance between the tuning fork and the observer at the instant when the apparent frequency becomes maximum is ......... $m$.

The pitch of the whistle of an engine appears to drop by $20 \%$ of its original value when it passes a stationary observer. If the speed of sound in air is $350 \ m/s$,then the speed of the engine in $m/s$ is:

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

$A$ train whistling at a constant frequency $n_0$ is moving towards a station at a constant speed $v$. The train passes a stationary observer on the station. The frequency $n$ of the sound as heard by the observer is plotted as a function of time $t$. Identify the expected curve.