Suppose that the speed of sound in air at a given temperature is $400 \ m/s$. An engine blows a whistle at $1200 \ Hz$ frequency. It is approaching an observer at the speed of $100 \ m/s$. What is the apparent frequency as heard by the observer in $Hz$?

$A$ speeding motorcyclist sees a traffic jam ahead. He slows down to $36\, km\, h^{-1}$. He finds that the traffic has eased and a car moving ahead of him at $18\, km\, h^{-1}$ is honking at a frequency of $1392\, Hz$. If the speed of sound is $343\, m s^{-1}$,the frequency of the honk as heard by him will be .... $Hz$.

An observer moves towards a stationary source of sound with a velocity one-fifth of the velocity of sound. The percentage change in the apparent frequency is ..... $\%$

$A$ rocket is moving at a speed of $200\; m s^{-1}$ towards a stationary target. While moving, it emits a wave of frequency $1000\; Hz$. Some of the sound reaching the target gets reflected back to the rocket as an echo. Calculate:
$(1)$ the frequency of the sound as detected by the target and
$(2)$ the frequency of the echo as detected by the rocket.

$A$ train standing at the outer signal of a railway station blows a whistle of frequency $400 \ Hz$ in still air. The train begins to move with a speed of $10 \ ms^{-1}$ towards the platform. What is the frequency of the sound for an observer standing on the platform (in $Hz$)? (Sound velocity in air $= 330 \ ms^{-1}$).

If a source emitting waves of frequency $f$ moves towards an observer with a velocity $v/4$ and the observer moves away from the source with a velocity $v/6$,the apparent frequency as heard by the observer will be ($v =$ velocity of sound).