A spelunker (cave explorer) drops a stone from rest into a hole. The speed of sound is 343 m/s in air, and the sound of the stone striking the bottom is heard 3.87 s after the stone is dropped. How deep is the hole?
d = 343m/s * 3.87s = 1327.4m.
Wrong. Not all of the 3.87 seconds is sound travel time. Most of it isnt
To determine the depth of the hole, we can use the equation for distance:
d = v * t
Where:
d = distance
v = velocity
t = time
Given:
v = 343 m/s (speed of sound)
t = 3.87 s (time taken for the sound to be heard)
First, we need to find the time it takes for the stone to reach the bottom of the hole. Since both the stone and the sound waves travel at the same velocity, we can assume the time it takes for the stone to reach the bottom is also 3.87 s.
Now, we can calculate the distance using the equation:
d = v * t
= 343 m/s * 3.87 s
Calculating this:
d = 1,329.41 m
Therefore, the depth of the hole is approximately 1,329.41 meters.
To determine the depth of the hole, we need to calculate the time it took for the stone to reach the bottom and then use that time to find the distance traveled using the speed of sound.
First, let's find the time it took for the stone to reach the bottom. We have the time of 3.87 seconds for the sound to reach the surface. Since sound velocity is the same in both directions (upwards and downwards), this time is equal to the time it took for the stone to fall plus the time it took for the sound to travel back up.
Since the stone was dropped from rest, we only need to consider the time it took for the sound to travel back up. Therefore, we need to divide the total time (3.87 seconds) by 2.
Time taken by the stone to reach the bottom: 3.87 s / 2 = 1.935 s
Now, we can calculate the distance traveled by the stone using the equation:
distance = speed * time
The speed of sound is given as 343 m/s, and the time taken by the stone to reach the bottom is 1.935 seconds.
Distance = 343 m/s * 1.935 s = 664.305 m
Therefore, the depth of the hole is approximately 664.305 meters.