Karen shouts across a canyon and hears an echo 3.1 s later.
How wide is the canyon? The speed of
sound is 343 m/s.
Answer in units of m
distance=speedsound*time
2*width=343*3.1
To calculate the width of the canyon, we need to consider the time it takes for Karen's shout to reach the other side and bounce back as an echo.
Given:
Time taken to hear the echo (t) = 3.1 s
Speed of sound (v) = 343 m/s
Since the sound travels to the other side and back, the total distance traveled by sound is twice the width of the canyon.
We can use the formula:
Distance (d) = Speed (v) * Time (t)
Substituting the values:
Distance (d) = 343 m/s * 3.1 s
= 1063.3 m
However, this total distance traveled by sound includes both the distance to the other side and the distance back, so we need to divide it by 2 to get the width of the canyon.
Width of the canyon = Distance traveled by sound / 2
= 1063.3 m / 2
= 531.65 m
Therefore, the width of the canyon is approximately 531.65 meters.
To determine the width of the canyon, we can use the speed of sound and the time it takes for the echo to reach Karen.
First, let's understand the concept of an echo. When sound waves travel through the air, they bounce off objects and reflect back to the source, creating an echo. The time taken for the sound to travel to the object and back to the source can give us a clue about the distance between the source and the object.
In this case, Karen shouts across the canyon and hears an echo 3.1 seconds later. This time interval represents the round trip time for the sound wave to go from Karen to the canyon wall and bounce back to Karen.
The speed of sound is given as 343 m/s. Since the sound wave has to travel twice the distance, we need to divide the measured time (3.1 s) by 2.
Time taken for one-way trip = (Time for echo / 2) = 3.1 s / 2 = 1.55 s
Now, we can calculate the width of the canyon using the formula:
Distance = Speed × Time
Distance = 343 m/s × 1.55 s = 531.65 m
Therefore, the width of the canyon is approximately 531.65 meters.