Two friends $A$ and $B$ are standing a distance $x$ apart in an open field and wind is blowing from $A$ to $B$. $A$ beats $a$ drum and $B$ hears the sound $t_{1}$ time after he sees the event. $A$ and $B$ interchange their positions and the experiment is repeated. This time $B$ hears the drum $t_{2}$ time after he sees the event. Calculate the velocity of sound in still air $v$ and the velocity of win $u$. Neglect the time light takes in travelling between the friends.
Initially, resultant velocity of sound $=\mathrm{v}+\mathrm{u}$
Later, resultant velocity of sound=v-u
Add (i) and (ii)
$V=\frac{x}{2}\left(t_{1}+\frac{1}{t_{2}}\right)$
and
$u=\frac{x}{2}\left(\frac{1}{t_{1} t_{2}}\right)$
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