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 durm and hears the sound $t_1$ time after he sees the event. A and B interchange their positions and the experiment is reoeated . This time B hears the drum $t_2$ time after be sees the event. Calculate the velocity of sound in still Air v and the velocity of wind u. Neglect the time light takes in travelling between the friends.

Answer 1

Let velocity of sound = V

Velocity of air = u

Distance between A and B = x

In the first case, resultant of sound = u+v

$\Rightarrow (v+u)t_1=x$

$\Rightarrow v+u=\frac{x}{t_1}$ .....(i)

In the second case, resultant velocity of sound

= v-u\\

$\therefore (v-u)t^2=x$

$\Rightarrow v-u=\frac{x}{t^2}$ ....(ii),

From equations (i) and (ii),

From equation (i)

u =$\frac{x}{t_1}-v=\frac{x}{2t^1}-\frac{x}{2T_2}$

= $\frac{x}{2t_1}-\frac{x}{2t_2}$

= $\frac{x}{2}(\frac{1}{t^1}-\frac{1}{t^2})$

$\therefore$ Velocity of air V = $\frac{x}{2}(\frac{1}{t_1}-\frac{1}{t^2})$

and Velocity of wind

u = $\frac{x}{2}(\frac{1}{t_1}-\frac{1}{t^2})$