Full picture for resonance/open/closed pipes

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dartmed

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Ok, I just don't understand open and closed pipes. I get the general equation, but I can't seem to grasp the entire picture. Can anyone what this concept even entails and when we would have to use it? What does it tell us? How does this relate to longitudinal waves? What does resonance have to do with any of this? Are open and closed pipes applicable to only standing waves?

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Ok, I just don't understand open and closed pipes. I get the general equation, but I can't seem to grasp the entire picture. Can anyone what this concept even entails and when we would have to use it? What does it tell us? How does this relate to longitudinal waves? What does resonance have to do with any of this? Are open and closed pipes applicable to only standing waves?

There is a node at closed ends and antinode at open ends.

Let's picture this now.

If the pipe has two closed ends, there can be increments of HALF a wavelength in there because the wave must go from node to node.

If the pipe has two open ends, there can be increments of HALF a wavelength in there because the wave must go from antinode to antinode.

If the pipe has one closed end, one open end, there can be increments of a QUARTER of a wavelength because the waves must only go from node to antinode.

In the first resonance, the wavelength is as large as possible and the frequency is as small as possible.

Now with closed/closed or open/open, the LONGEST wavelength that can fit in there is TWICE the length of the pipe. (Because you only need to go from one node to the next.)

With closed/open, the LONGEST wavelength that can fit in there is FOUR TIMES the length of the pipe. (Because you only need to go from one node to antinode.)
 
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