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 ... $m/s$.

$A$ 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 $350\,m/s$)

An engine is moving with uniform speed along a circular track emitting a sound of frequency $400\, Hz$ as shown in the figure. The speed of the engine is $30\, m/s$ and the speed of sound is $330\, m/s$. An observer is standing inside the track. The maximum frequency observed by the observer 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 approaching a railway crossing at a speed of $120 \ km/h$ sounds a whistle of frequency $576 \ Hz$,when it is $288 \ m$ away from the crossing. The frequency heard by an observer standing on the road perpendicular to the track at a distance of $384 \ m$ from the crossing is (Speed of sound in air $= 340 \ m/s$): (in $Hz$)

The Doppler effect is applicable for