Question

Suppose A nad B in the previous problem change their positions in such a way that tha 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 beasting by A ?

Answer 1

Given, velocity of sound = v

Velocity of air = u

Velocity of sound be in direction AVC,

So that it can reach B with result velocity.

Angle between v and u is, $\theta >\frac{\pi }{2}$

Resulatant,$\overrightarrow{AD}=\sqrt{(v^2-u^2)}$

Here time taken by light to reach 'B' is negleated :

$\therefore$ TIme lag between seeing and hearing

= time to here the drum sound

t =$\frac{\text{D}isplacement}{\text{V}elocity}$

$\frac{x^2}{\sqrt{v^2-u^2}}$

= $\frac{x}{\sqrt{(v+u)(v-u)}}$

= $\frac{x}{\sqrt{\left(\frac{x}{t_1}\right)\left(\frac{x}{t_2}\right)}}=\sqrt{t_1{t}_2}$