if you shout into the grand canyon your voice travels at the speed of sound (340 m/s) to the bottom if the canyon and back and you hear an echo how deep is the grand canyon at a spot where you can hear your echo 5.2 seconds after you shout
To determine the depth of the Grand Canyon at the spot where you can hear your echo 5.2 seconds after you shout, we can use the speed of sound formula: distance = speed × time.
Since the sound travels from you to the bottom of the canyon and back, the total distance covered is twice the depth of the canyon.
Let's denote the depth of the canyon as "d" in meters. The total distance covered by sound is 2d.
Given that the speed of sound is 340 m/s and the time is 5.2 seconds, we can set up the equation:
2d = 340 m/s × 5.2 s
Simplifying:
2d = 1768 m
Dividing both sides by 2:
d = 884 m
Therefore, at the spot where you can hear your echo 5.2 seconds after you shout, the depth of the Grand Canyon is approximately 884 meters.