$A$ 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 $= 330 \,ms^{-1}$).

An engine whistling at a constant frequency $n_0$ and moving with a constant velocity goes past a stationary observer. As the engine crosses him,the frequency of the sound heard by him changes by a factor $f$. The actual difference in the frequencies of the sound heard by him before and after the engine crosses him is

$A$ 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 $340\; m s^{-1}$.

$A$ 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 $Hz$)?

Two sources of sound $S_1$ and $S_2$ produce sound waves of same frequency $660\, Hz$. $A$ listener is moving from source $S_1$ towards $S_2$ with a constant speed $u\, m/s$ and he hears $10\, \text{beats/s}$. The velocity of sound is $330\, m/s$. Then, $u$ equals ... $m/s$.

When a train approaches a stationary observer,the apparent frequency of the whistle is $n'$ and when the same train recedes away from the observer,the apparent frequency is $n''$. Then,the apparent frequency $n$ when the observer moves with the train is