Two friends A and B are standing a distance x
Question:

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 $\mathrm{t}_{2}$ 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.

Solution:

Initially, resultant velocity of sound $=v+u$

$(v+u)=\frac{x}{t_{1}}$……..(i)

Later, resultant velocity of sound=v-u

$(v-u)=\frac{x}{t_{1}}$…………(ii)

Add (i) and (ii)

$V=\frac{x}{2}\left(t_{1}+\frac{1}{t_{2}}\right)$

and

$u=\frac{x}{2}\left(t_{1} t_{z}\right)$

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