Question

Karen shouts across a canyon and hears an echo 7.5 s later. how wide is the canyon? the speed of sound is 343 m/s. answer in units of m.

Answer 1

After Karen shouts, the sound wave of her voice travels across the canyon, it hits the walls, and then it comes back to Karen in a total time of t=7.5 s. If we call L the distance between Karen and the other side of the canyon (so, L is the width of the canyon), it means that the sound wave covers a distance of S=2L in this time.
Since the wave moves by uniform motion, we can use the usual relationship between space, time and velocity:

`v= (S)/(t)= (2L)/(t)`
where v=343 m/s is the speed of sound. Using this number, we can find L from the previous equation:

`L= (vt)/(2)= ((343 m/s)(7.5 s))/(2)=1286 m`
So, the canyon is 1286 meters wide.