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Given any musical instrument, when a note is played on the instrument, does the fundamental have only one node and 2 antinodes (Theoretically fundamental frequencies should have half wavelength)? If yes what factor in the instrument allows it to create such a wave(like length of string )?

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In short, no. If you take a tube, closed at both ends (or opened at both ends, depending if you are talking about nodes of pressure, or nodes of displacements), the fundamental will indeed have an anti-node and two nodes.

However, there are instruments which are making the sound from tubes closed at one end (the organ for instance). In that case, the fundamental frequency will have one node, and one anti-node.

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    Exactly the example I was going to cite. You could also include bells, plates, and other 2D vibrating systems, or stiff bars with various boundary conditions. You may also want to mention that for the half closed tube the fundamental wavelength is 4*L. – user50691 Jan 19 at 15:34
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    @ggcg Yes, there are a lot of examples! I wanted to keep it short however, and answer "only" the: "Do all fundamental frequencies have 1 anti-node and 2 nodes", No. Bells are also a great example I agree, but it is more complicated to describe what is happening in there! – Tom Jan 19 at 15:44
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    @hanceldsouza yes, overtones will have more antinodes, but there are not the fundamental, there are overtones/harmonics: their frequency is usually a multiple of the fundamental. I suggest reading the whole wiki article I linked, schemes are good and it's pretty complete :). Overtones are treated also! – Tom Jan 19 at 16:17
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    @hanceldsouza an overtone would be expected to have more nodes and anti-nodes than the fundamental. The fundamental will generally be the longest/simplest waveform that can be established in the resonator. – topo Reinstate Monica Jan 19 at 16:18
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    @hanceldsouza, I think you are confusing the individual harmonics supported by the string or pipe with the complex wave formed by exciting it. The question is asking about the individual modes. (I see you asked the question, so perhaps with this new info you can reformulate it) – user50691 Jan 20 at 0:52

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