A boy shouts while standing between two walls. He heard two echoes with an interval of $0.25 s$ in between them. If he is $60 m$ away from the farthest wall, how far away is he from the other wall?
[speed of sound $= 344 m s^{- 1}$ ]

36 m

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34 m

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17 m

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40 m

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Solution

The correct option is C $17 m$
Given:
Speed of sound, $v = 344 m s^{- 1}$

The distance of the boy from the left wall is $x$ , the total distance travelled by the sound for the first echo is: $s_{1} = 2 x m$
$2 x = 344 \times t_{1}$ ......(1)

The distance of boy from the farthest wall is $60 m$ , the total distance travelled by the sound for the second echo is:
$s_{2} = 120 m$
$120 = 344 \times t_{2}$ ......(2)

Time difference between the first and the second echo, $t_{2} - t_{1} = 0.25 s$

Substracting both equations:
$120 - 2 x = 344 t_{2} - 344 t_{1}$
$120 - 2 x = 344 (t_{2} - t_{1})$
$120 - 2 x = 344 \times 0.25$
$2 x = 120 - 86$
$2 x = 34$
$x = 17 m$

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A boy shouts while standing between two walls. He heard two echoes with an interval of 0.25 s in between them. If he is 60m away from the farthest wall, how far away is he from the other wall? [speed of sound = 344 ms−1]

A boy shouts while standing between two walls. He heard two echoes with an interval of $0.25 s$ in between them. If he is $60 m$ away from the farthest wall, how far away is he from the other wall?
[speed of sound $= 344 m s^{- 1}$ ]