Two cars are moving towards each other at the speed of $50 \,m/s$. If one of the cars blows a horn at a frequency of $250 \,Hz$, the wavelength of the sound perceived by the driver of the other car is (Speed of sound in air $= 350 \,m/s$) (in $\,cm$)

$A$ whistle producing sound waves of frequencies $9500 \ Hz$ and above is approaching a stationary person with speed $v \ ms^{-1}$. The velocity of sound in air is $300 \ ms^{-1}$. If the person can hear frequencies up to a maximum of $10,000 \ Hz$,the maximum value of $v$ up to which he can hear the whistle is ... $ms^{-1}$.

$A$ bus is moving with a velocity of $5 \, ms^{-1}$ towards a huge wall. The driver sounds a horn of frequency $165 \, Hz$. If the speed of sound in air is $335 \, ms^{-1}$, the number of beats heard per second by the passengers in the bus will be:

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 $= 330 \,m/s$):

$A$ 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.

The driver of a car travelling with a speed $V_1 \ m/s$ towards a wall sounds a siren of frequency $n \ Hz$. If the velocity of sound in air is $V \ m/s$,then the frequency of sound reflected from the wall and as heard by the driver,in $Hz$,is