On a hiking trip you are walking through a canyon with verti

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 1.9 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.

Solution

suppose one is at distance d1 and other is at d2 from you.

then time taken by first echo = distance / time

t1 = 2d1 / 343

for 2nd echo :

t2 = 2d2 / 343

for 3rd echo\"

distance willbe = d1 + d1 + d2 + d2 = 2 (d1 + d2)

t3 = 2(d1+ d2) / 343

and t2 - t1 = 1.9 sec

(2d2 / 343) - (2d1 / 343) = 1.9

2(d2 - d1) = 343 x 1.9

d2 -d1 = 325.85 ........(i)

and t3 - t2 = 0.9

(2(d1+ d2) / 343 ) - (2d2 / 343 ) = 0.9

2d1 / 343 = 0.9

d1 = 154.35 m

and putting in (i)

d2 - 154.35 = 325.85

d2 = 480.2 m

width L = d1 +d2 = 480.2 +154.35 =   634.55 m