$A$ 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 $330 \, m/s$,the speed of the car will be ..... $m/s$.

$A$ source of sound $S$ is moving with a velocity $50 \ m/s$ towards a stationary observer. The observer measures the frequency of the source as $1000 \ Hz$. What will be the apparent frequency of the source when it is moving away from the observer after crossing him? The velocity of sound in the medium is $350 \ m/s$.

$A$ train is moving with a uniform speed $33 \ m/s$ and an observer is approaching the train with the same speed. If the train blows a whistle of frequency $1000 \ Hz$ and the velocity of sound is $333 \ m/s$, then the apparent frequency of the sound that the observer hears is: (in $Hz$)

When both source and listener are approaching each other,the observed frequency of sound is given by (where $V$ is the speed of sound,$V_L$ and $V_S$ are the velocities of the listener and source respectively,and $n_0$ is the radiated frequency):

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 $ms^{-1}$)?

Consider two tuning forks with natural frequency $250 \,Hz$. One is moving away and another is moving towards a stationary observer at the same speed. If the observer hears beats of frequency $5 \,Hz$, then the speed of the tuning fork is: (Given, speed of sound wave is $350 \,m/s$.) (in $\,m/s$)