# Using Waves to Find Depth of Well

• rockerdude1210
In summary: I completely agree that hints can sometimes obscure important lessons, but they can also be a valuable tool when used sparingly. Hints should only be given if the student is still not getting the idea or if they are struggling with a problem.
rockerdude1210

## Homework Statement

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A student uses an audio oscillator of adjustable frequency to measure the depth of a dried up well. Two successive resonances are heard at 17.0Hz and 23.8Hz. The speed of sound in air is 343 m/s. How deep is the well?

f=nv/4L

## The Attempt at a Solution

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I solved the problem and the answer was 25.22m. However, I got this answer by using the equation for a tube open at both ends. I was confused because I thought that the correct equation would have been the one for a tube open at one end and closed at the other. Can someone explain why f=nv/2L was used instead of f=nv/4L

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You can and should use the closed ended pipe formula - did you try it?
Remember that n in the closed pipe formula, can only take odd-number values.

Yes, I tried it (f=nv/4L) with n equal to one and the online assignment page said that it was wrong and then when I used the open-open formula (f=nv/2L) with n equal to one, the website said that the answer was correct. I was assuming that it was an error with the answer, but I just wanted to make sure.

The assignment does not appear to be in error - you will get the same result using the correct equation provided you understand what you are doing.

For a closed tube resonator, if the first frequency is the nth harmonic, then the next freqeuncy will be the (n+2)th harmonic. The difference between them will be given by:
$$f_{n+2}-f_n = \frac{(n+2)v}{4L} - \frac{nv}{4L} = \frac{v}{2L}$$

But for an open open tube, the nth harmonic is followed by the (n+1)th harmonic - so the difference becomes:
$$f_{n+1}-f_n = \frac{(n+1)v}{2L}-\frac{nv}{2L} = \frac{v}{2L}$$
... exactly the same value.

The hint was trying to get you to realize that there was a shortcut.

Thank you!

I can't believe I missed that, it seems so simple now.

This is why it is important to understand the relations instead of just learning to use the equations.
In general, you should not follow a hint blindly - it should give you that "ah-ha!" moment at some stage.
If that does not happen, then go back to working without the hint.

I don't like to give out hints in my coursework because they can obscure important lessons.
i.e. Without the hint you'd probably have figured out that the question had set you up with two equations with two unknowns (n and L) then you solve by simultaneous equations to find L.

## 1. How does using waves help determine the depth of a well?

Using waves to find the depth of a well involves sending sound or electromagnetic waves down into the well and measuring the time it takes for the waves to bounce back to the surface. By knowing the speed of the waves and the time it takes for them to travel, the depth of the well can be calculated using a simple equation.

## 2. What types of waves are typically used for this process?

The most commonly used waves for finding the depth of a well are sound waves and electromagnetic waves. Sound waves are used in sonar technology, where a pulse of sound is sent down into the well and the echoes are received and measured. Electromagnetic waves, such as radar or microwaves, can also be used to find the depth of a well by measuring the time it takes for the waves to reflect off the well walls and return to the surface.

## 3. Are there any limitations to using waves to find the depth of a well?

Yes, there are some limitations to this method. The accuracy of the results can be affected by factors such as the composition and shape of the well, the type of waves used, and any obstructions or irregularities in the well. It is also important to note that this method can only be used for wells that are deep enough for the waves to travel and reflect back to the surface.

## 4. What are the advantages of using waves to find the depth of a well?

Using waves to find the depth of a well is a non-invasive and relatively quick method compared to other techniques such as drilling or manual measurements. It also allows for remote measurement, meaning the operator does not need to physically access the well. Additionally, this method can provide accurate results for both shallow and deep wells.

## 5. Is this method used for any other applications besides finding the depth of a well?

Yes, the use of waves to measure depth is not limited to wells. This method is also used in various other applications such as oceanography, geophysics, and archaeology. It can be used to measure the depth of bodies of water, underground structures, and even the composition of layers beneath the Earth's surface.

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