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where n is an integer number, and that produces 1st harmonic, 2nd harmonic, so on.

But what about if only one end is fixed and the other is not? (like jiggling a ripe tied with a loop to a pole such that the loop can move up and down)?

How is their relationship defined then?

I know that the closed end still remains as a node, but the other end will now be an antinode instead of a node

so would it be

wavelength = 2xlength / n-0.5?

since there's 0.5 less "loops" produced?