How deep is the well using the speed of sound?

  • Thread starter starji
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In summary, using the speed of sound, we can determine the depth of a well by calculating the time it takes for a sound to travel from the bottom of the well to the surface. By using the equation t=d/342.8 + sqrt(d/4.9), we can solve for the distance d. This can be done by making the substitution x = sqrt(d) and using the quadratic formula to solve for x, then squaring it to find the final distance d.
  • #1
starji
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how deep is the well? (using speed of sound)

Homework Statement


A boy drops a penny into a deep well. if he hears the splash 5.0 seconds after he releases the penny, how deep is the well? (assume the well is 20degrees C) (also assume there is no air resistance)


Homework Equations


speed of sound: v=331+0.59T and basic kinematics


The Attempt at a Solution


i've found the speed of sound to be 342.8m/s

if t=d/v then the time it takes the sound of the splash to reach the boy's ears is t=d/342.8

the time it takes for the penny to drop into the well is: d=vit+0.5at^2; the vi is 0 so d=4.9t^2 therefore the time it take the penny to drop is t=sqrt(d/4.9)

so from here i should be able to find the distance by 5=d/342.8+ sqrt(d/4.9), but it isn't working and I am getting tiny numbers
 
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  • #2
Your method looks okay. Perhaps you could show the steps you've taken to solve your last equation for d.
 
  • #3
oh ok sry here it is: d=vit+0.5at^2; d=0+0.5(9.8)t^2; d=4.9t^2
 
  • #4
So far, so good. Now make the substitution: x = sqrt(d), and use the quadratic formula to find x. Then square x to get d.
 
  • #5
wait what? i don't really understand where x is coming from or how that would work since i get x^2=4.9t^2 leaving me with 2 variables and no way to use the quad formula
 
  • #6
Sorry, I was referring to the last equation you presented in your first post. The working up to that point is correct: now you need to solve that equation for d. I suggest making the substitution x = sqrt(d).
 
  • #7
oh ok good call thanks i'll try it
 

FAQ: How deep is the well using the speed of sound?

1. How deep is the well?

The depth of a well can vary greatly depending on factors such as location, geology, and purpose. In general, a residential well can range from 100-500 feet deep, while a commercial or industrial well can be as deep as 2000 feet.

2. What is the average depth of a well?

The average depth of a well is around 300 feet. However, this can vary significantly depending on the type of well, as well as the location and geology of the area.

3. How is the depth of a well determined?

The depth of a well is determined by drilling into the ground until water is reached. The drilling process may involve taking soil samples and performing tests to determine the ideal depth for accessing clean and sustainable water.

4. Can a well be too deep?

Yes, a well can be too deep. If a well is drilled too deep, it may encounter underground rock formations or other barriers that prevent water from flowing freely. It is important to consult with a professional when determining the appropriate depth for a well.

5. What is the deepest well ever drilled?

The deepest well ever drilled is the Kola Superdeep Borehole, located in Russia. It was drilled to a depth of 7.5 miles (12.2 kilometers) and was intended to reach the Earth's mantle. However, the project was ultimately discontinued due to technical difficulties and budget constraints.

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