$A$ motorcycle starts from rest and accelerates along a straight path at $2 \; m/s^2$. At the starting point of the motorcycle,there is a stationary electric siren. How far has the motorcycle gone when the driver hears the frequency of the siren at $94 \%$ of its original value (in $; m$)? (Speed of sound $= 330 \; m/s$)

$A$ 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 ..... $m/s$.

$A$ police car moving at $22 \,ms^{-1}$ chases a motorcyclist. The policeman sounds a horn at $176 \,Hz$, while both of them move towards a stationary siren of frequency $165 \,Hz$. If the number of beats heard by the motorcyclist per second is zero, then the speed of the motorcycle is (Speed of sound in air $= 330 \,ms^{-1}$) (in $\,ms^{-1}$)

Two stationary sources each emit waves of wavelength $\lambda$. An observer moves from one source to the other with velocity $u$. The number of beats heard by the observer 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 $\,ms^{-1}$)

$A$ source of sound is moving towards a stationary observer with $\frac{1}{10}$ of the speed of sound. The ratio of apparent to real frequency is