1.1.4 | revision #15580 | Savchenko Solutions

Statement

1.1.4. Three microphones located on the same straight line at points $$A$$ , $$B$$ , $$C$$ recorded successively at the moments $$t_A > t_B > t_C$$ the sound of an explosion that occurred at point $$O$$ , which lies on the segment $$AC$$ . Find the length of the segment $$AO$$ if $$AB = BC = L$$ . At what point in time did the explosion occur?

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Solution

1. Let us introduce the following variables

$$$x_B=L-x$$$

$t_A=t_B+\Delta t$

2. Time of flight of $\gamma$ -quantum to counters

$t_B+\Delta t=\frac{x}{c}$

$t_B=\frac{L-x}{c}$

3. Solving the equations together, we obtain

$\frac{L-x}{c} + \Delta t = \frac{x}{c}$

$x= \frac{L+c\Delta t}{2}=1.15\text{ m}$

Answer

At a distance $1.15\text{ m}$ from the microphone $$A$$