Question

if you shout into the grand canyon, your voice travels at the speed of sound (340 m/s) to the bottom of 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?

Explanation:

Step1: Recall the speed - distance - time formula

The formula is $d = vt$, where $d$ is distance, $v$ is speed, and $t$ is time. The time given is the time for the sound to travel to the bottom and back. So the time for the sound to travel just to the bottom of the canyon is half of the total time.

Step2: Calculate the one - way time

The total time $t_{total}=5.2$ s. The one - way time $t=\frac{t_{total}}{2}=\frac{5.2}{2}=2.6$ s.

Step3: Calculate the depth of the canyon

The speed of sound $v = 340$ m/s. Using the formula $d = vt$, we substitute $v = 340$ m/s and $t = 2.6$ s. So $d=340\times2.6 = 884$ m.

Answer:

884 m