Question

If, standing on the edge of a narrow canyon, you shout and hear your echo in 4.0 s, how far away is the canyon wall? The temperature of the air is 20°C.

Answer 1

4.0 s is the time between the shout and the echo, so it corresponds to the time it takes for the sound wave to travel from our mouth to the wall of the canyon, and then to come back. If we call L the width of the canyon, it means that t=4.0 s is the time the sound wave takes to cover a distance of 2L. The speed of sound at
`20^(\circ)C` is v=343 m/s, so we have:

`v= (2L)/(t)`
from which we find L:

`L= (vt)/(2)= ((343 m/s)(4.0 s))/(2) =686 m`
So, the distance of the canyon wall from us is 686 m.