When a train approaches a stationary observer,the apparent frequency of the whistle is $n'$ and when the same train recedes away from the observer,the apparent frequency is $n''$. Then,the apparent frequency $n$ when the observer moves with the train is

$A$ car blowing a horn of frequency $350\, Hz$ is moving towards a wall with a speed of $5\, m/s$. The beat frequency heard by a person standing between the car and the wall is ..... $Hz$ (speed of sound in air $= 350\, m/s$).

$A$ train,standing at the outer signal of a railway station,blows a whistle of frequency $400\; Hz$ in still air.
$(i)$ What is the frequency of the whistle for a platform observer when the train $(a)$ approaches the platform with a speed of $10\; m s^{-1}$,$(b)$ recedes from the platform with a speed of $10\; m s^{-1}$?
$(ii)$ What is the speed of sound in each case? The speed of sound in still air can be taken as $340\; m s^{-1}$.

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 of frequency $500 \, Hz$ tied to the end of a string of length $1.2 \, m$ revolves at $400 \, rev/min$. $A$ listener standing some distance away in the plane of rotation of the whistle hears frequencies in the range (speed of sound $= 340 \, m/s$):

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: