Why does end correction in pipes change with radius

In summary, the concept of end correction in closed pipes is commonly accepted as being approximately 0.6 times the radius of the pipe. This is due to the vibration of sound particles at the opening of the pipe, which changes the acoustical length of the pipe. However, there is limited information available on why this specific value is used. In a closed pipe resonating at its first harmonic, the air particles at points A are not moving much, while the particles at points B are moving the most. It is unclear whether these particles will move laterally to points C or back into the pipe at point D. The distance that these particles travel is affected by the energy of the particles at point B, but it is the extra traveling
  • #1
Tyrone Sawyer
3
0
This being WRT resonating pipes. Apparently the acoustical length of the pipe is different to the physical length due to the vibration of the sound particles moving the particles at the opening so that the physical length is no longer the length of resonance.

I've found many sources on the broad topic on end correction, and I know that it's commonly accepted that the end correction of a closed pipe is ~0.6*r, where r is the radius of the pipe. I've been doing some research, and I really can't understand why this is the case, however, no matter where I search, I can't find any sources on the topic.

P.S any sources would be greatly welcomed!
 
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  • #2
That makes some sense, but I'm still a little confused... Say I have the following closed pipe resonating at it's first harmonic:
_______________..D
|A.....B...C
|A.....B...C
|A____________B...C
......D
Then, as I understand it, the air particles at points A aren't moving, or they aren't moving much, and the air particles at points B are moving the most. Will those particles be moving laterally to points C? Or will they also move to points D? When they move to point D, do they move back into the pipe? If so, than that means that those particles will have traveled over a greater area with a pipe with a greater radius, yes, but I don't see how that actually increases the distance that the particles are traveling. Wouldn't that distance just be affected by the energy of the particles B as they're being displaced? It is the extra traveling distance of the vibrating particles outside of the length of the pipe which creates end correction, no?
 

What is end correction in pipes?

End correction in pipes refers to the adjustment that needs to be made to the theoretical length of a pipe to account for the effects of the pipe walls. This correction is necessary because sound waves travel through the air inside the pipe, and the physical presence of the pipe walls can impact the length of the pipe needed to produce a certain frequency of sound.

Why does end correction vary with pipe radius?

The end correction in pipes varies with the pipe radius because the size of the pipe affects the speed at which sound waves travel through it. The larger the pipe radius, the slower the sound waves will travel, and the more pronounced the end correction will be. This is because the larger radius allows for more air molecules to be displaced, resulting in a longer effective length of the pipe.

How does end correction impact the resonance of a pipe?

End correction can significantly impact the resonance of a pipe. If the end correction is not properly accounted for, the pipe may not produce the expected frequency of sound. This can result in a distorted sound or an inability to produce certain pitches. By properly adjusting for end correction, the pipe will resonate at the desired frequency and produce a clear, accurate sound.

What are some factors that can affect end correction in pipes?

Aside from pipe radius, there are other factors that can influence end correction in pipes. These include the material of the pipe, the shape of the pipe (cylindrical or conical), and the temperature and humidity of the air inside the pipe. All of these factors can impact the speed at which sound waves travel through the pipe and, therefore, affect the end correction calculation.

How do scientists calculate end correction in pipes?

Calculating end correction in pipes involves using mathematical formulas and experimental data to determine the appropriate adjustment to the theoretical length of the pipe. These calculations take into account factors such as pipe radius, material, and shape, as well as the speed of sound in the given conditions. Advanced techniques, such as finite element analysis, can also be used to calculate end correction with greater accuracy.

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