Two stationary sources each emit waves of wavelength $\lambda$. An observer moves from one source to the other with velocity $u$. The number of beats heard by the observer is:

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

$A$ 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 $\,ms^{-1}$)

An observer standing at a station observes a frequency of $219 \, Hz$ when a train approaches and $184 \, Hz$ when the train goes away from him. If the velocity of sound in air is $340 \, m/s$,then the velocity of the train and the actual frequency of the whistle will be:

$A$ vehicle with a horn of frequency $n$ is moving with a velocity of $30\, m/s$ in a direction perpendicular to the straight line joining the observer and the vehicle. The observer perceives the sound to have a frequency $n + n_1$. Then (if the sound velocity in air is $300\, m/s$):

$A$ person driving a car at a constant speed of $15\,m/s$ is approaching a vertical wall. The person notices a change of $40\,Hz$ in the frequency of his car's horn upon reflection from the wall. The frequency of the horn is ............ $Hz$. (Given: Speed of sound: $330\,m/s$)