Question

Suppose A and B in the previous problem 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 B finds between seeing and hearing the drum beating by A?

Answer 1

The time B finds among seeing and hearing the drum beating by A is  $t=\sqrt{t_{1} t_{2}}$

Explanation:

Step 1:

Given

Velocity of sound = $v m/s$

Velocity of air = $u m/s$

Speed of sound be in course ABC , so it can arrive at B with resultant speed.

Angle between v and u is $\theta>\pi / 2$

Resultant $\mathrm{AD}=\sqrt{v^{2}-u^{2}}$

Step 2:

Here time taken by light to arrive at B is neglect.

∴Time log among seeing and hearing =time to here the drum sound

$\text {time}=\frac{\text {displacement}}{\text {velocity}}$

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

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

$t=\frac{x}{\sqrt{\left(\frac{x}{t_{1}}\right)\left(\frac{x}{t_{2}}\right)}}$

Step 3:

Speed is given by the following

$\text { speed }=v+u=\frac{\text { distance }}{\text { time }}=\frac{x}{t_{1}}$

$v-u=\frac{x}{t_{2}}$

$t=\sqrt{t_{1} t_{2}}$

∴ The time B finds among seeing and hearing the drum beating by A is

$t=\sqrt{t_{1} t_{2}}$