Open pipe end correction distance for waves

In summary, Struggling to find the correct resonances for a close end pipe. The resonance for the longer tube would look something like this, with a smaller random error.
  • #1
Bolter
262
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Homework Statement
See below
Relevant Equations
frequency = speed/wavelength
Screenshot 2020-03-12 at 17.10.40.png

Struggling on how to do this Q

I have tried drawing a sketch of it and had come up with this

IMG_4076.JPG


This is probably not right, as the speed of sound is not given here as well the length of the open pipe tube?

Any help would be really great! Thanks
 
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  • #2
One end is not open. There is a piston. That will affect both end correction and resonant length.

Ps. Why do they give you two resonances?
 
  • #3
Merlin3189 said:
One end is not open. There is a piston. That will affect both end correction and resonant length.

Ps. Why do they give you two resonances?

If it is a close end pipe, then the sketch should look like this then

IMG_4077.JPG


I'm not so sure why myself of why they give 2 resonance here

What do I make out of the 2 resonant lengths given here?
 
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  • #4
Well, what will the diagram look like for the longer tube resonance?

What do you know about the difference between the two lengths?
 
  • #5
Merlin3189 said:
Well, what will the diagram look like for the longer tube resonance?

What do you know about the difference between the two lengths?

The resonance for the longer tube would look something like this?

CC01F886-40BB-4819-80A1-32BE88D9399B.jpeg


And the difference between these 2 lengths is half the wavelength in mm
 
  • #6
So there you are.
 
  • #7
Merlin3189 said:
So there you are.

Ok thanks I’m sort of getting it but when I do this

94BC5007-B8A3-4601-A30C-521F31A1C816.jpeg


What do I choose my pipe length, L to be?
 
  • #8
I must let L be 240.3mm to get a end correction, e to be 0.01165m right?

8BD9F37E-1FBD-47B4-9DD4-2BB81B357493.jpeg
 
  • #9
Yes. You could have used the longer one, but that would have been 3λ/4 rather than λ/4

So now you can calculate the speed of sound. Perhaps that's why they didn't mention it?

BTW
If this had been a real experiment, they wouldn't have given the same answer of course, because neither would be exactly right. And you wouldn't know which was better. I'd choose the longer one, because the ±1mm or whatever your measurement error is, would make less % error on the longer measurement.

I seriously can't believe anyone could possibly locate these resonances as precisely as they claim.
What any normal person would do, is to, preferably find more resonances and also take several measurements at each one to get an average and an estimate of the random error.
 
Last edited:
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1. What is an open pipe end correction distance for waves?

The open pipe end correction distance for waves is the distance between the end of an open pipe and the nearest node of a standing wave. It is an important factor in determining the resonant frequency of a pipe and can affect the quality of sound produced.

2. How is the open pipe end correction distance calculated?

The open pipe end correction distance can be calculated using the formula L = 0.6D, where L is the correction distance and D is the diameter of the pipe. This formula is based on experimental data and may vary slightly depending on the shape and material of the pipe.

3. Why is the open pipe end correction distance important?

The open pipe end correction distance is important because it affects the resonant frequency of a pipe. If the correction distance is not taken into account, the calculated resonant frequency may be inaccurate, resulting in a different pitch or tone than expected.

4. How does the open pipe end correction distance affect sound quality?

The open pipe end correction distance can affect the quality of sound produced by a pipe. If the correction distance is too small, the resonant frequency will be higher than expected, resulting in a higher pitch and potentially a thinner or more nasal sound. If the correction distance is too large, the resonant frequency will be lower than expected, resulting in a lower pitch and potentially a muffled or dull sound.

5. Are there any other factors that can affect the open pipe end correction distance?

Yes, there are other factors that can affect the open pipe end correction distance, such as the temperature and humidity of the surrounding air. These factors can cause the pipe to expand or contract, changing the correction distance and potentially altering the resonant frequency of the pipe.

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