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 1.7 s after the first, and the third echo arrives 0.9 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.

Explanation / Answer

Sound travels in both directions

Suppose, let us say you are d1 distance from 1 side of wall and d2 from other side of wall

So , width of canyon , w = d1 + d2

Let us say d1 < d2

Time taken for 1st echo , t1 = 2d1 / s

where s = speed of sound = 343 m/s

Time at which second echo is heard , t2 = t1 + 1.7 = 2 d2 / s

Time at which 3rd echo is heard, t3 = t2 + 0.9 = t1 + 2.6 = 2(d1+d2)/s

2d1/s + 1.7 = 2d2/s

d2 - d1 = 1.7*s/2 = 1.7*343/2 = 291.55 m

2(d1+d2)/s = 2d1/s + 2.6

2 d2/s = 2.6

d2 = 1.3*s = 1.3*343 = 445.9 m

d1 = d2 - 291.55 = 445.9 - 291.55 = 154.35 m

Width of the canyon = d1 + d2 = 154.35 + 445.9 = 600.25 m

Related Questions

Navigate

• Browse (All)
• Browse O
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.