An observer starts moving with uniform acceleration $a$ towards a stationary sound source of frequency $f$. As the observer approaches the source,the apparent frequency $f'$ heard by the observer varies with time $t$ as:

$A$ stationary source is emitting sound at a fixed frequency $f_0$,which is reflected by two cars approaching the source. The difference between the frequencies of sound reflected from the cars is $1.2 \%$ of $f_0$. What is the difference in the speeds of the cars (in $km/h$) to the nearest integer? The cars are moving at constant speeds much smaller than the speed of sound,which is $330 \ m/s$.

$A$ and $B$ are two sources generating sound waves. $A$ listener is situated at $C$. The frequency of the source at $A$ is $500 \, Hz$. $A$ now moves towards $C$ with a speed of $4 \, m/s$. The number of beats heard at $C$ is $6$. When $A$ moves away from $C$ with a speed of $4 \, m/s$,the number of beats heard at $C$ is $18$. The speed of sound is $340 \, m/s$. The frequency of the source at $B$ is ..... $Hz$.

$Assertion :$ The Doppler formula for sound waves is symmetric with respect to the speed of the source and the speed of the observer.
$Reason :$ The motion of a source with respect to a stationary observer is not equivalent to the motion of an observer with respect to a stationary source.

$A$ source of sound $S$ is moving with a velocity $50 \ m/s$ towards a stationary observer. The observer measures the frequency of the source as $1000 \ Hz$. What will be the apparent frequency of the source when it is moving away from the observer after crossing him? The velocity of sound in the medium is $350 \ m/s$.

$A$ train is moving with a uniform speed $33 \ m/s$ and an observer is approaching the train with the same speed. If the train blows a whistle of frequency $1000 \ Hz$ and the velocity of sound is $333 \ m/s$,then the apparent frequency of the sound that the observer hears is: (in $Hz$)