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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?
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Solution
Given:
Distance between A and B = x
Let v be the velocity of sound in the direction along line AC.
Let u be the velocity of air in the direction along line AB.
Angle between v and u = θ > \[\frac{\pi}{2}\]
Resultant velocity of sound and air that will reach B = \[\vec{AD} = \sqrt{\left( \text{ v } ^2 - \text{ u } ^2 \right)}\]
Here, the time taken by light to reach B is neglected.
∴ Time lag between seeing and hearing = Time taken to hear the sound of the drum
\[t = \frac{\text{ Displacement } }{\text{ Velocity } }\]
\[ = \frac{x}{\sqrt{\text{ v } ^2 -\text{ u } ^2}}\]
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