If you shout across a canyon and hear the echo 0.42 s later, how wide is the canyon?

To determine the width of a canyon using the echo, you need to measure the time it takes for the sound to travel to the other side and back (also known as the round trip time). In this case, the echo is heard 0.42 seconds after shouting.

The speed of sound in air is approximately 343 meters per second. So, for the sound to travel to the other side of the canyon and back, it covers twice the distance of the canyon width.

To calculate the canyon's width, you can use the formula:

Width = (Speed of Sound × Round Trip Time) / 2

Plugging in the values, we get:

Width = (343 m/s × 0.42 s) / 2

Simplifying this, we find:

Width = 72.18 meters

Therefore, the width of the canyon is approximately 72.18 meters.