$A$ train approaching a railway platform with a speed of $20 \, m \, s^{-1}$ starts blowing the whistle. The speed of sound in air is $340 \, m \, s^{-1}$. If the frequency of the emitted sound from the whistle is $640 \, Hz$,the frequency of sound as heard by a person standing on the platform is .... $Hz$.

Two sources of sound $S_1$ and $S_2$ produce sound waves of same frequency $660\, Hz$. $A$ listener is moving from source $S_1$ towards $S_2$ with a constant speed $u\, m/s$ and he hears $10\, \text{beats/s}$. The velocity of sound is $330\, m/s$. Then, $u$ equals ... $m/s$.

$A$ siren placed at a railway platform is emitting sound of frequency $5 \text{ kHz}$. $A$ passenger sitting in a moving train $A$ records a frequency of $5.5 \text{ kHz}$ while the train approaches the siren. During his return journey in a different train $B$,he records a frequency of $6.0 \text{ kHz}$ while approaching the same siren. The ratio of the velocity of train $B$ to that of train $A$ is

$A$ car sounding a horn of frequency $1000 \,Hz$ passes a stationary observer. The ratio of frequencies of the horn noted by the observer before and after passing of the car is $11:9$. The speed of the car is (Speed of sound $v = 340 \,ms^{-1}$) (in $\,ms^{-1}$)

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.

$A$ 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 = $320 \, m/s$)