You drop a stone down a well. You hear the splash 2.23 s later. How deep is the well? speed of sound 343 m/s
Well, don't stone me for this, but let's do some calculations!
We know that the speed of sound is 343 m/s. So, in 2.23 seconds, the sound traveled a distance of 343 m/s * 2.23 s = 764.89 meters.
Now, hold your breath because we're diving into some math. The stone needs to fall from the top of the well and the sound needs to climb back up, so the total distance traveled is twice the depth of the well.
So, the depth of the well is 764.89 meters / 2 = 382.44 meters.
Voila! The well is approximately 382.44 meters deep. Hope this answer didn't make you "well"ow with laughter!
To determine the depth of the well, we can use the equation:
d = v * t
Where:
d = depth of the well
v = speed of sound = 343 m/s
t = time taken for the sound to reach your ears = 2.23 s
By substituting the given values into the equation, we can solve for the depth of the well:
d = 343 m/s * 2.23 s
d ≈ 764.89 m
Therefore, the depth of the well is approximately 764.89 meters.
To calculate the depth of the well, you can use the equation:
depth = (speed of sound) * (time traveled by sound) / 2
Let's substitute the given values into the equation:
depth = (343 m/s) * (2.23 s) / 2
Now, we can solve this equation:
depth = 384.89 m
Therefore, the depth of the well is approximately 384.89 meters.
Let the depth be X.
2.23 s = sound travel time + drop time
X/343 + sqrt(2X/g) = 2.23
Convert to a quadratic equation and solve for X.
(22.3 - X/343)^2 = X/4.9
Here is an iterative method instead:
Since the stone is much slower than sound, most of the 2.23 seconds will be spent with the stone falling. If it falls for 2.1 s, the well depth is 21.6 meters. The time for the sound to arrive would then be 0.063 s. The total time to hear the sound would be 2.16 s. That is not long enough. If the stone falls 2.16 s, a distance of 22.8 m, the sound returns in 0.066 s. That makes the total time about right.