Two whistles $A$ and $B$ produce notes of frequencies $660 \ Hz$ and $596 \ Hz$ respectively. There is a listener at the mid-point of the line joining them. Now,the whistle $B$ and the listener start moving with a speed of $30 \ m/s$ away from the whistle $A$. If the speed of sound is $330 \ m/s$,how many beats will be heard by the listener?

The apparent frequency of a note,when a listener moves towards a stationary source with a velocity of $40 \ m/s$,is $200 \ Hz$. When the listener moves away from the same source with the same speed,the apparent frequency of the same note is $160 \ Hz$. The velocity of sound in air is (in $m/s$):

An observer is moving towards a stationary source of sound. In this case:

$A$ police car moving at $22 \,ms^{-1}$ chases a motorcyclist. The policeman sounds a horn at $176 \,Hz$, while both of them move towards a stationary siren of frequency $165 \,Hz$. If the number of beats heard by the motorcyclist per second is zero, then the speed of the motorcycle is (Speed of sound in air $= 330 \,ms^{-1}$) (in $\,ms^{-1}$)

$A$ vehicle sounding a whistle of frequency $256 \,Hz$ is moving on a straight road towards a hill with a velocity of $10 \,ms^{-1}$. The number of beats per second observed by a person travelling in the vehicle is (velocity of sound $= 330 \,ms^{-1}$).

Two cars $A$ and $B$ are moving away from each other in opposite directions. Both cars are moving with a speed of $20 \, ms^{-1}$ with respect to the ground. If an observer in car $A$ detects a frequency of $2000 \, Hz$ from the sound source in car $B$,what is the natural frequency of the sound source of car $B$ (in $Hz$)? (Speed of sound in air $= 340 \, ms^{-1}$)