Two sirens situated one kilometer apart are producing sound of frequency $330 \ Hz$. An observer starts moving from one siren to the other with a speed of $2 \ m/s$. If the speed of sound is $330 \ m/s$,what will be the beat frequency heard by the observer?

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

Two trains $A$ and $B$ are moving towards each other with speeds $72 \ km/h$ and $36 \ km/h$ respectively. The train $A$ whistles at $640 \ Hz$ frequency. Before the trains meet,the frequency of sound heard by a passenger in Train $B$ is (Speed of sound in air $= 340 \ m/s$). (in $Hz$)

$A$ siren placed at a railway platform is emitting a sound of frequency $5 \text{ kHz}$. $A$ passenger sitting in a moving train $A$ records the frequency of the siren as $5.5 \text{ kHz}$. During his return journey by train $B$,he records the frequency of the siren as $6 \text{ kHz}$. The ratio of the speed of train $B$ to that of train $A$ is

An engine is moving on a circular path of radius $200 \,m$ with a speed of $15 \,m/s$. What will be the frequency heard by an observer who is at rest at the centre of the circular path,when the engine blows the whistle with a frequency of $250 \,Hz$?

$A$ police van,moving at $22 \, m/s$,chases a motorcyclist. The policeman sounds a horn at $176 \, Hz$,while both of them move towards a stationary siren of frequency $165 \, Hz$ as shown in the figure. If the motorcyclist does not observe any beats,his speed must be .... $m/s$ (take the speed of sound $= 330 \, m/s$).