$A$ source of sound of frequency $640 \,Hz$ is moving at a velocity of $\frac{100}{3} \,m/s$ along a road, and is at an instant $30 \,m$ away from a point $A$ on the road. $A$ person standing at $O$, $40 \,m$ away from the road, hears sound of apparent frequency $v^{\prime}$. The value of $v^{\prime}$ is (velocity of sound $= 340 \,m/s$): (in $\,Hz$)

$A$ man is standing between two trains moving away from and towards him,both with a speed of $4 \, m/s$. If both trains produce a sound of frequency $240 \, Hz$,calculate the number of beats heard by the man. (Speed of sound in air = $320 \, m/s$)

Two cars $A$ and $B$ are moving away from each other in opposite directions. Both cars are moving with a speed of $20 \, ms^{-1}$ with respect to the ground. If an observer in car $A$ detects a frequency of $2000 \, Hz$ from the sound source in car $B$,what is the natural frequency of the sound source of car $B$ (in $Hz$)? (Speed of sound in air $= 340 \, ms^{-1}$)

$A$ 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 $= 330 \ ms^{-1}$).

Statement $-1$: Due to the motion of the listener,the frequency of the sound waves (as received by the listener) emitted by a stationary source is affected.
Statement $-2$: Due to the motion of the source,the wavelength of the sound waves (emitted by the source) as received by a stationary listener is affected.
Statement $-3$: If the receiver and the source are both moving,the observed frequency must be different from the original frequency of the source.
Treat the motion of the source or listener as always along the line joining them for all the above cases.

An observer is approaching with a speed $v$ towards a stationary source emitting sound waves of wavelength $\lambda_0$. The wavelength shift detected by the observer is (Take $c$ as the speed of sound).