Two cars $A$ and $B$ are moving in the same direction with speeds $36 \, km/hr$ and $54 \, km/hr$ respectively. Car $B$ is ahead of $A$. If $A$ sounds a horn of frequency $1000 \, Hz$ and the speed of sound in air is $340 \, m/s$,the frequency of sound received by the driver of car $B$ is ................. $Hz$.

Two persons $A$ and $B$, each carrying a source of sound of frequency $n$, are standing a few metres apart in a quiet field. $A$ starts moving towards $B$ with a speed $u$. If $v$ is the speed of sound, the number of beats heard per second by $A$ will be

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).

$A$ car is moving with a speed of $72 \text{ km/h}$ towards a roadside source that emits sound at a frequency of $850 \text{ Hz}$. The car driver listens to the sound while approaching the source and again while moving away from the source after crossing it. If the velocity of sound is $340 \text{ m/s}$, the difference of the two frequencies the driver hears is: (in $\text{ Hz}$)

An observer and a source emitting sound of frequency $120 \,Hz$ are on the $X$-axis. The observer is stationary while the source of sound is in motion given by the equation $x=3 \sin \omega t$ (where $x$ is in metres and $t$ is in seconds). If the difference between the maximum and minimum frequencies of the sound observed by the observer is $22 \,Hz$,then the value of $\omega$ is (speed of sound in air $=330 \,ms^{-1}$):

$A$ whistle sends out $256$ waves in a second. If the whistle approaches the observer with a velocity equal to $\frac{1}{3}$ of the velocity of sound in air,calculate the number of waves per second the observer will receive.