If you shout across a canyon and hear the echo 0.57 s later, how wide is the canyon?
96.9
To calculate 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 in air is approximately 343 meters per second.
Given that the time it takes for the echo to return is 0.57 seconds, we can use the following formula:
Distance = Speed × Time
Distance = 343 m/s × 0.57 s
Distance ≈ 195.51 meters
Therefore, the width of the canyon is approximately 195.51 meters.
To determine 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 varies depending on several factors, including temperature, humidity, and altitude. On average, at sea level and room temperature (around 20° Celsius or 68° Fahrenheit), the speed of sound is approximately 343 meters per second (or about 1125 feet per second).
Given that we hear the echo 0.57 seconds later, we can calculate the total time it takes for the sound to travel from the initial shout, reach the other side of the canyon, and return as an echo. Since the sound travels to the other side of the canyon and back, we can divide the total time by 2 to get the one-way time.
So, the one-way time is 0.57 seconds divided by 2, which is equal to 0.285 seconds.
Now, we can multiply the one-way time by the speed of sound to determine the distance traveled by sound in that time:
Distance = Speed of sound x Time
Distance = 343 m/s x 0.285 s
Therefore, the width of the canyon is approximately 97.755 meters (or 320.129 feet).
2*Width = (sound speed)*(0.57 s)
The sound speed depends upon temperature but is about 340 m/s
Solve for the width. I hope you see why the factor 2 is needed.