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 1.5 safter 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.

Answer 1

Supposeone is at distance d₁ and other is at d₂ from you.

then time taken by first echo = distance / time

t₁ = 2d₁ / 343

For the second echo:

The distance will be = d₁ + d₁ + d₂ + d₂ = 2 (d₁ + d₂)

t₃ = 2(d₁+ d₂) / 343

and t₂ - t₁ = 1.5 sec

(2d₂ / 343) - (2d₁ / 343) = 1.5

2(d₂ - d₁) = 343 x 1.5

(d₂ - d₁) = 514.5 / 2

(d₂ - d₁) = 257.25 ------- (1)

and t₃ - t₂ = 0.5

(2(d₁+ d₂) / 343 ) - (2d₂ / 343 ) = 0.5

2d₁ / 343 = 0.5

d₁ = 85.75 m

From (1),

d₂ - d₁ = 257.25

d₂ = 257.25 + 85.75

d₂ = 343 m

The width of the canyon, L = d₁+ d₂

L = 85.75 m + 343 m

L a= 428.75 m