On a hiking trip, you are walking through a canyon with vertical walls and are c

Question

On a hiking trip, you are walking through a canyon with vertical walls and are closer to one wall than the other. Having taken Physics, you decide to determine the width of the canyon by using your knowledge of kinematics and the speed of sound. You shout "Hey" as loud as you can, and after a short time you hear three echoes. The second echo arrives 1.3 s after the first, and the third echo arrives 0.5 s after the second. Assuming that the speed of sound is 343 m/s and that there are no reflections of sound from the ground, find the width of the canyon.
_____ m

Explanation / Answer

Let

d1 = the distance of the nearer wall
d2 = distance of the farther wall
d1 + d2 = width of the canyon

Thus,

2d2/v - 2d1/v = 1.3 s

2(d1 + d2)/v - 2d2 / v = 0.5 s

Thus,

d1 = 85.75 m

d2 = 308.7 m

Thus, the width of the canyon is

d1 + d2 = 394.45 m   [ANSWER]

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