$A$ person carrying a whistle emitting a note of $272 \text{ Hz}$ is running towards a reflecting surface with a speed of $18 \text{ km/h}$. The speed of sound in air is $345 \text{ m/s}$. The number of beats heard by him is:

$A$ police car with a siren of frequency $8 \ kHz$ is moving with uniform velocity $36 \ km/h$ towards a tall building which reflects the sound waves. The speed of sound in air is $320 \ m/s$. The frequency of the siren heard by the car driver is (in $kHz$)

$A$ source of sound emitting a note of frequency $200 Hz$ moves towards an observer with a velocity $v$ equal to the velocity of sound. If the observer also moves away from the source with the same velocity $v$,the apparent frequency heard by the observer is .... $Hz$

When the observer moves towards a stationary source with velocity $V_{1}$,the apparent frequency of the emitted note is $F_{1}$. When the observer moves away from the source with velocity $V_{1}$,the apparent frequency is $F_{2}$. If $V$ is the velocity of sound in air and $F_{1} / F_{2} = 2$,then $V / V_{1}$ is equal to:

Which pre-assumptions are used for the Doppler effect?

$A$ train,standing at the outer signal of a railway station,blows a whistle of frequency $400\; Hz$ in still air.
$(i)$ What is the frequency of the whistle for a platform observer when the train $(a)$ approaches the platform with a speed of $10\; m s^{-1}$,$(b)$ recedes from the platform with a speed of $10\; m s^{-1}$?
$(ii)$ What is the speed of sound in each case? The speed of sound in still air can be taken as $340\; m s^{-1}$.