$A$ man is standing between two trains moving away from and towards him,both with a speed of $4 \, m/s$. If both trains produce a sound of frequency $240 \, Hz$,calculate the number of beats heard by the man. (Speed of sound in air = $320 \, m/s$)

The apparent frequency of a sound wave as heard by an observer is $10\%$ more than the actual frequency. If the velocity of sound in air is $330 \, m/s$,then
$(i)$ The source may be moving towards the observer with a velocity of $30 \, m/s$
$(ii)$ The source may be moving towards the observer with a velocity of $33 \, m/s$
$(iii)$ The observer may be moving towards the source with a velocity of $30 \, m/s$
$(iv)$ The observer may be moving towards the source with a velocity of $33 \, m/s$

An observer is standing $500 \,m$ away from a vertical hill. Starting between the observer and the hill, a police van sounding a siren of frequency $1000 \,Hz$ moves towards the hill with a uniform speed. If the frequency of the sound heard directly from the siren is $970 \,Hz$, the frequency of the sound heard after reflection from the hill (in $Hz$) is about, (velocity of sound $= 330 \,m/s$):

With what velocity an observer should move relative to a stationary source so that a sound of double the frequency of the source is heard by the observer?

$A$ train is approaching a platform with a speed of $10 \,ms^{-1}$ while blowing a whistle of frequency $340 \,Hz$. What is the frequency of the whistle heard by a stationary observer on the platform (in $\,Hz$)? (Given speed of sound $= 340 \,ms^{-1}$)

Two cars $A$ and $B$ are moving away from each other in opposite directions. Both cars are moving with a speed of $20 \, ms^{-1}$ with respect to the ground. If an observer in car $A$ detects a frequency of $2000 \, Hz$ from the sound source in car $B$,what is the natural frequency of the sound source of car $B$ (in $Hz$)? (Speed of sound in air $= 340 \, ms^{-1}$)