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 1.5 s after the first, and the third echo arrives 0.7 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.(m)

Solution

Consider yourself to be standing at distance a from one wall and the width of the canyon to be d

Now the 2nd echo has to travel to the wall and back so that we can hear it.
Then it has to travel to the opposite wall and back so that we get the 3rd echo.

Hence we can say that the sound travels a total of 2*d in (1.5+.9) = 2.4 s

That is, 2*d = 343 * 2.4
or, d = 343 * 1.2 = 411.6

Therefore the required width of the canyon is 411.6 m