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A guitar string exhibits standing wave patterns when its struck, some superposition of sines and cosines, a drum head exhibits a superposition of Bessel functions when its struck.

Is there any musical instrument that exists that itself, exhibits spherical harmonics in producing its sound?

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  • $\begingroup$ Possibly an ocarina? $\endgroup$ – probably_someone Oct 29 '18 at 20:35
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I'm not an expert, so I don't know if there's some kind of "baloon" which produces sound when it is deformed.

Anyways, any real ballon, or plastic bag, or whatever closed surface, can produce noise if chosen appropiately, and that exhibits spherical harmonics, provided that you don't break it and all that.

I don't know if this was useful, but at least you know what kind of "structure" of instrument you have to look for.

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  • $\begingroup$ I believe the hypothetical balloon-like instrument instrument should also have its surface fixed in a static manner, just as the guitar string and the drum head have their boundaries (ends of a string and the rim, respectively) fixed statically. But then it seems the visualization of spherical harmonics cannot come from deformation of the instrument itself. $\endgroup$ – wcc Oct 29 '18 at 17:49
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Every musical instrument radiates a three dimensional sound pressure pattern and it's actually useful to analyze or represents these through spherical harmonics especially in the far field.

For example an acoustic guitar gets excited through standing waves of the string, but most of the radiation actually happens through the guitar's top which has a very complicated three dimensional radiation pattern which lends itself well to spherical harmonics analysis

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