If you shout across a canyon and hear an echo 3.6 s later, how wide is the canyon?
2,448 meters.
To find the width of the canyon, we can use the speed of sound and the time it takes for the echo to return.
The speed of sound can be approximated as 343 meters per second in dry air at 20 degrees Celsius.
Since the sound wave has to travel from you to the canyon wall and then bounce back to you, the total distance traveled by the sound wave is twice the width of the canyon.
Let's set up the equation: 2 * width = speed of sound * time
Plugging in the values, we have 2 * width = 343 m/s * 3.6 s
Simplifying, we get 2 * width = 1234.8 m
Now, we can solve for the width of the canyon:
width = 1234.8 m / 2
width = 617.4 meters
Therefore, the width of the canyon is approximately 617.4 meters.
To determine the width of the canyon, we need to calculate the time it takes for the sound to travel to the canyon wall and back as an echo. The speed of sound in air is approximately 343 meters per second.
First, let's divide the total time by 2 to get the time it takes for the sound to travel from you to the canyon wall (one-way).
3.6 s / 2 = 1.8 s
Next, we can use the speed of sound formula to find the distance traveled:
Distance = Speed × Time
Distance = 343 m/s × 1.8 s
Distance ≈ 617.4 meters
Therefore, the estimated width of the canyon is approximately 617.4 meters.
distancesoundtravels=2w=velcoitysoun*time
solve for width of canyon, w.