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 ................. $Hz$.

$A$ source and a detector move away from each other in the absence of wind with a speed of $20 \, m/s$ with respect to the ground. If the detector detects a frequency of $1800 \, Hz$ of the sound coming from the source,then the original frequency of the source,considering the speed of sound in air to be $340 \, m/s$,will be (in $Hz$):

Two passenger trains moving with a speed of $108\, km/h$ cross each other. One of them blows a whistle whose frequency is $750\, Hz$. If the speed of sound is $330\, m/s$,then the passengers sitting in the other train,after the trains cross each other,will hear a sound whose frequency is .... $Hz$.

Which of the following statements is false?

Doppler shift in frequency does not depend upon:

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.