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Two friends A and B are standing at a distance x apart in an open field and wind is blowing at a constant velocity u from A to B. A beats a drum and B hears its sound time $t_{1}$ after he sees the event. A and B interchange their position and A beats the drum again. This time B hears the drum time $t_{2}$ after he sees the event. Neglect the time light takes in travelling between the friends. Wind is continuously blowing in the same direction. Choose the correct options.

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Velocity of wind, $u = x (\frac{1}{t_{1}} - \frac{1}{t_{2}})$

Velocity of sound in still air, $v = x (\frac{1}{t_{1}} + \frac{1}{t_{2}})$

Velocity of sound in still air, $v = \frac{x}{2} (\frac{1}{t_{1}} + \frac{1}{t_{2}})$

Velocity of wind, $u = \frac{x}{2} (\frac{1}{t_{1}} - \frac{1}{t_{2}})$

answer is B, C.

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Detailed Solution

$\frac{x}{v + u} = t_{1} \Rightarrow v + u = \frac{x}{t_{1}}; \frac{x}{v - u} = t_{2} \Rightarrow v - u = \frac{x}{t_{2}}$

$v = \frac{x}{2} (\frac{1}{t_{1}} + \frac{1}{t_{2}}); u = \frac{x}{2} (\frac{1}{t_{1}} - \frac{1}{t_{2}})$

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