The driver of a bus approaching a big wall notices that the frequency of his bus's horn changes from $420\, Hz$ to $490\, Hz$,when he hears it after it gets reflected from the wall. Find the speed of the bus (in $kmh^{-1}$) if the speed of sound is $330\, ms^{-1}$.

$A$ train,standing in a station-yard,blows a whistle of frequency $400\; Hz$ in still air. The wind starts blowing in the direction from the yard to the station with a speed of $10\; m s^{-1}$. What are the frequency,wavelength,and speed of sound for an observer standing on the station's platform? Is the situation exactly identical to the case when the air is still and the observer runs towards the yard at a speed of $10\; m s^{-1}$? The speed of sound in still air can be taken as $340\; m s^{-1}$.

Two whistles $A$ and $B$ each have a frequency of $500\,Hz$. $A$ is stationary and $B$ is moving towards the right (away from $A$) at a speed of $50\,m/s$. An observer is between the two whistles moving towards the right with a speed of $25\,m/s$. The velocity of sound in air is $350\,m/s$. Assume there is no wind. Then which of the following statements are true:

$A$ source with a frequency of $90 \, \text{vibrations/sec}$ moves towards a stationary observer with a velocity of $1/10 \, V$, where $V$ is the speed of sound. What frequency will the observer hear in $\text{vibrations/sec}$?

$A$ musician using an open flute of length $50\,cm$ produces second harmonic sound waves. $A$ person runs towards the musician from another end of a hall at a speed of $10\,km/h.$ If the wave speed is $330\,m/s,$ the frequency heard by the running person shall be close to...... $Hz$

$A$ source and an observer approach each other with the same velocity $50 \, m/s$. If the apparent frequency is $435 \, s^{-1}$,then the real frequency is .... $s^{-1}$ (Take speed of sound $v = 332 \, m/s$)