$A$ stationary source emits sound waves of frequency $500\, Hz$. Two observers moving along a line passing through the source detect sound to be of frequencies $480\, Hz$ and $530\, Hz$. Their respective speeds are,in $m\,s^{-1}$ (Given speed of sound $= 300\, m/s$)

$A$ motorcyclist is approaching a large wall with a velocity of $90\,km/hr$. $A$ car is chasing him with a velocity of $108\,km/hr$. If the car sounds a horn at $30\,Hz,$ the beat frequency heard by the motorcyclist is . . . . . . $Hz$. Take the velocity of sound $= 330\,m/s$.

$A$ train is moving along a semicircular track. The engine is at one end of the semicircular part of the track,while the last carriage is at the other end. The driver blows a whistle of frequency $200 \ Hz$. The velocity of sound is $340 \ m/s$. If the speed of the train is $30 \ m/s$,what is the apparent frequency observed by a passenger in the middle of the train (in $Hz$)?

$A$ man sitting in a moving train hears the whistle of the engine. The frequency of the whistle is $600 \ Hz$.

$A$ source and an observer approach each other with the same velocity $50 \, m/s$. If the apparent frequency is $435 \, s^{-1}$,then the real frequency is .... $s^{-1}$ (Take speed of sound $v = 332 \, m/s$)

$A$ source of sound is moving with a constant velocity of $30 \,m/s$ emitting a note of frequency $256 \,Hz$. The ratio of frequencies observed by a stationary observer while the source is approaching him and after it crosses him is [speed of sound in air $= 330 \,m/s$].