Calculating the Depth of a Well: Stone Drop and Sound Splash Time

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In summary, the stone is dropped into the well and the sound of the splash is heard 2.3 seconds later. The depth of the well is 9.8 meters.
  • #1
green11
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Homework Statement



A stone is dropped into a well. The sound of the splash is heard 2.30 s later. What is the depth of the well?


Homework Equations



g = -9.8 m/s^2
Vsound in air = 343 m/s

The Attempt at a Solution



I'm not really sure how to start. I know that the time it takes to drop down + the time it takes the sound to go back up must = 2.3 seconds
 
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  • #2
<< two threads merged by berkeman >>
 
Last edited by a moderator:
  • #3
Well, write out what else you know. What do you know about the distance the stone must fall and the distance the sound waves must travel? What about the time it takes the rock to fall a distance h?
 
  • #4
For the future, please do not post your homework questions in multiple forums.
 
  • #5
green11 said:
I know that the time it takes to drop down + the time it takes the sound to go back up must = 2.3 seconds
Try writing an equation for that. I'd suggest using variables like [itex]t_\text{drop}[/itex] [itex]t_\text{sound}[/itex].
 
  • #6
jgens said:
For the future, please do not post your homework questions in multiple forums.
I'm sorry. I posted it in here first then realized it might better belong in the other one.
 
  • #7
diazona said:
Try writing an equation for that. I'd suggest using variables like [itex]t_\text{drop}[/itex] [itex]t_\text{sound}[/itex].


[itex]t_\text{drop}[/itex] + [itex]t_\text{sound}[/itex] = 2.3 s

Like that?
 
  • #8
jgens said:
Well, write out what else you know. What do you know about the distance the stone must fall and the distance the sound waves must travel? What about the time it takes the rock to fall a distance h?

The distance the stone falls = The distance the sound waves travel

Also, I know that the equation for free fall distance is:
h = (1/2)(-9.8)t^2

Rearranging this, I got that t = sqrt(-h/4.9)
 
  • #9
So, from your other thread you said,

trock + tsound = 2.3

You have an expression trock. Knowing that the sound waves must travel a distance h with velocity v = 343 m/s can you complete the equation?
 
  • #10
jgens said:
So, from your other thread you said,

trock + tsound = 2.3

You have an expression trock. Knowing that the sound waves must travel a distance h with velocity v = 343 m/s can you complete the equation?

Would that just be

sqrt(-h/4.9) + 343h = 2.3 s ??
 
  • #11
Not quite. Since you're only worried about magnitudes here, we don't need to worry about h being positive or negative, so your equation should read,

2.3 s = sqrt(h/g) + h/vs

Remember t != v(h), t = h/v or h = vt.
 
  • #12
Thank you!
 

1. How do you calculate the depth of a well using the stone drop method?

The depth of a well can be calculated by dropping a stone into the well and measuring the time it takes for the stone to hit the water. The formula for calculating the depth is: depth = (gravity x time squared) / 2. However, this method may not be accurate due to factors such as wind resistance and water resistance.

2. What is the sound splash time method for calculating the depth of a well?

The sound splash time method involves dropping an object into the well and measuring the time it takes for the sound of the splash to reach the surface. The formula for calculating the depth using this method is: depth = (speed of sound x time) / 2. This method can be more accurate than the stone drop method, but it also has limitations such as variations in the speed of sound.

3. What factors can affect the accuracy of calculating the depth of a well using these methods?

There are several factors that can affect the accuracy of these methods, including wind resistance, water resistance, variations in the speed of sound, and the precision of the timing device used. It is important to consider these factors and make adjustments to the calculations accordingly.

4. How can you improve the accuracy of calculating the depth of a well using these methods?

To improve the accuracy of these methods, it is important to use a high-quality timing device, take multiple measurements and calculate an average, and account for any external factors that may affect the results. It is also recommended to use both methods and compare the results for a more precise measurement.

5. Are there any other methods for calculating the depth of a well?

Yes, there are other methods for calculating the depth of a well, such as using a measuring tape or a depth finder. These methods may be more accurate and reliable, but they also require specialized equipment and may not be feasible for all situations.

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