Two friends A and B are standing a distance x apartin an open field and wind is blowing from A to B.A beats a drum and B hears the sound `t_1` timed after he sees the event. A and B intechange their positions and te experiment is repeated. This time B hears teh drum `t_2` time after he sees the event. Calculte teh velocity of sound in still air v and the velocity of wind u. Neglect the tiem light takes in travelling between the friends.

Answer

A, B

Explanation

Let velocity of sound = v
Velocity of air = u
Distance between A and B = x
IN te first case , resultant of sound `=u+v`
`rarr (v+u)t_1 =x`
` rarr v+u = x/t_1` …..i

IN the second case, resultant velocity of sound
`= v-u`
`:. (v-u)t_2 = x`
`rarr v-u= x/t_2 .......ii.`
From equation i. and ii.,
`2v= x/t_1+x/t_2`
`= (x/t_1+x/t_2)`
`rarr v= x/2 (1/t_1 +1/t_2)`
From equation i,
`u=x/t_1-v=x/(2t_1)-x/(2t_2)`
`= x/2 (1/t_1- /t_2 )`
`:` Velocity of air `v= x/2 (1/t_1 - 1/t_2)`
and Velocity of wind
`u= x/2 ( 1/t_1 - 1/t_2)`.