4. If you shout across a canyon and hear an echo 3.0 s later , how wide is the canyon?
Well, if I were to answer that question seriously, I would say that the distance between you and the canyon walls would be approximately 531 meters, assuming the speed of sound is around 343 meters/second. But let's not be serious! How wide is the canyon? Well, it's so wide that even a gazillion clowns juggling while riding unicycles couldn't jump across it! Or maybe it's so wide that it would take a lifetime to walk from one side to the other. Either way, it's a big ol' canyon!
To determine the width of the canyon, we need to calculate the time it takes for the sound to travel to the opposite side of the canyon and back (round trip time).
Since the echo is heard 3.0 seconds later, it means that the sound traveled to the opposite side and returned in that time. Therefore, the round trip time is 3.0 seconds.
Since sound travels at a speed of approximately 343 meters per second in air, we can use this information to find the width of the canyon.
Let's assume the width of the canyon is represented by "d" meters.
So, the time it takes for the sound to travel from your location to the opposite side of the canyon is d/343 seconds.
Similarly, the time it takes for the echo to reach your location from the opposite side of the canyon is also d/343 seconds.
Adding these two times together, we get:
d/343 + d/343 = 3.0
Combining like terms:
2d/343 = 3.0
To isolate "d", we can multiply both sides of the equation by 343 and divide by 2:
d = (3.0 * 343) / 2
Simplifying:
d = 514.5 meters
Therefore, the width of the canyon is approximately 514.5 meters.
To determine the width of the canyon, you need to calculate the round-trip travel time for the sound wave. This involves the time it takes for the sound to travel from you to the canyon wall and then back to you as an echo.
Since the sound wave travels to the canyon wall and back, the total time it takes for the echo to reach you is twice the time it takes for the sound to reach the canyon wall.
Given that you hear the echo 3.0 seconds later, the time it takes for the sound to reach the canyon wall is half of that, which is 1.5 seconds.
Now, to calculate the distance, you need to know the speed at which sound travels. The speed of sound in air is approximately 343 meters per second. So, multiplying the speed of sound by the time it takes for the sound to reach the canyon wall will give you the distance.
Distance = speed of sound × time
Distance = 343 m/s × 1.5 s
Distance = 514.5 meters
Therefore, the width of the canyon is approximately 514.5 meters.
So,
v= d/t/
d= (343 m/s) (1.5 s) = 228.6 m