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` timed after he sees the event. A and B interchange their positions and the experiment is repeated. The velocity of sound in still air is `v` and the velocity of wind is `u`. This time B hears the drum `t_2` time after he sees the event. Suppose A and B change their positions in such a way that the line joining them becomes perpendicular to the direction of wind while maintaining the separation `x`. What will be the time lag B finds between seeing and hearing the drum beating by A?

Answer

B

Explanation

Given velocity of sound = v
velocity of air = u
velocity of sound be in direction AVC,
so that it can reach B with resultant velocity,
Angle between v and u is `theta gtpi/2`
ltbr Resultant `vec(AD) = sqrt(v^2-u^2)`
Here time taken by lilght to reach B is neglected:
`:.` Time lag betwen seeing and hearing
= time to here the drum sound
`t= Displancement /velocity `
`= x^2/(sqrt(v^2-u^2))`
`= x/(sqrt((v+u)(v-u))`
`=x/(sqrt(x/t_1)(x/t_2))`
from question 49
`=sqrt(t_1 t_2)`.