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Many musical instruments use resonance tubes with one closed end - all brass instruments (I think), clarinet, etc. There are also instruments where both ends are open (flute, pipes) Are there any which use two closed ends, that is, a resonance tube with nodes at both ends?

I am aware of the problems which would exist for such an instrument - essentially not be very loud - but I am just curious if anyone knows of any.

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It was already mentioned by Carl Witthoft, but I think the ocarina does count, as long as you're not too hung up on the resonance chamber being a tube as such. From Wikipedia:

The ocarina, unlike other vessel flutes, has the unusual quality of not relying on the pipe length to produce a particular tone. Instead the tone is dependent on the ratio of the total surface area of opened holes to the total cubic volume enclosed by the instrument.[6] This means that, unlike a flute or recorder, sound is created by resonance of the entire cavity and the placement of the holes on an ocarina is largely irrelevant – their size is the most important factor.

The holes have to be there to let the air out of course, and they affect the pitch, but the mechanism isn't the same as for a flute or recorder with an open end.

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  • $\begingroup$ Well, as I mentioned about percussion instruments I was thinking of instruments that can be roughly modeled as closed-closed resonance tubes, which the Ocarina cannot. But, I would say this class of flute is the closet I will get. $\endgroup$
    – levitopher
    Apr 2 '14 at 16:59
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Well, does playing flute-like across the top of a beer bottle count? Or, better put: a jug-player in a country "Jug band" plays his instrument that way.

It's also your call whether blocked instruments with holes along the length qualify, such as an ocarina. I sort of guess what you're looking for is an instrument with an air pocket as the resonance, as opposed to, say, the resonance of a solid xylophone bar. You could try taping over the F-holes in a violin :-), or even worse, a trombonist using a plunger mute!

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    $\begingroup$ A beer bottle is a closed-open instrument, so is not what I'm looking for. (not that familiar with Ocarina but I think that is also closed-open). I guess "air pocket" is pretty accurate - I would accept an instrument with other holes to make the notes as long as the ends were closed, I think. That seems like the same level of complication as suggesting that a Clarinet is "just a half-open tube." $\endgroup$
    – levitopher
    Apr 1 '14 at 1:32
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You don't explicitly state you are looking for a wind instrument so perhaps a drum would count. Perhaps a snare drum since the snare is on the resonant (non-struck) head or a kettle drum maybe qualifies as a pitched instrument.

If you are looking for a wind instrument in particular and Carl Witthoft's suggestions of the ocarina or the jug do not fit the bill, I think the answer must be no as you are not leaving much opportunity to energise the resonant tube or air pocket.

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  • $\begingroup$ <en.wikipedia.org/wiki/Timpani> Occasionally tympani or kettle drums are re-tuned while playing to perform a "glissando". $\endgroup$
    – baldrik
    Apr 2 '14 at 6:21
  • $\begingroup$ I was not thinking of percussion instruments because of the overtones are not pure - not that they are pure on wind instruments either, but the vibrating heads on percussion instruments have a very complex set of oscillations so modeling them as closed tubes wouldn't make sense. $\endgroup$
    – levitopher
    Apr 2 '14 at 16:57
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Unlike flutes which have an antinode at the blown end, reed instruments can have either a node or antinode at the reed end. Clarinets have a node, while saxophones have an antinode. Reed instruments, however, always seem to have an antinode at the far end. If one were to construct a reed instrument with a node at the far end that had just enough of a hole to allow for a net flow of air through the instrument, as well as a node at the reed end, it would generate the same set of harmonics as an instrument with antinodes at both ends.

For the benefit of anyone confused by "node" and "anti-node", a sound wave consists of a velocity wave and a pressure wave. For the wave to reverse direction, one or the other must flip (flipping both would leave the sound traveling in the original direction). A node flips the velocity wave, while an anti-node flips the pressure wave.

If a pipe has a node at one end and an anti-node at the other, then after one round trip, both pressure and velocity waves will have flipped; after a second round trip, they will have been flipped back. For the wave to get back to its original state thus requires two round trips.

If a pipe has anti-nodes at both ends, one round trip will flip the pressure wave twice without flipping the velocity wave at all. Thus, the wave will get back to its original state after only one round trip.

If one were to construct a pipe with a node at both ends, one round trip would flip the velocity wave without flipping the pressure wave at all. The wave would thus get back to its original state after only one round trip. This wouldn't really be workable if one used the most common form of node (a closed pipe end) since there would be way of stimulating the air in a completely closed pipe, but if might be possible if one or both ends used a reed or diaphragm.

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  • $\begingroup$ That is an incredible answer that I wish I was smart enough to understand, or even craft an instrument to test your theory. $\endgroup$ Jan 22 at 13:39
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    $\begingroup$ @AdamBarnes: See my addendum. $\endgroup$
    – supercat
    Jan 22 at 16:46

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