I’m working on a novel musical instrument that will be made with metal (brass, aluminum,…) round bars. I’m looking for a formula that will give the note (frequency) for a given metal, length and diameter. I have been away from Physics for decades. Is there such a thing? Thank you in advance
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2$\begingroup$ It will matter how the bars are held in place, and how you will make them vibrate, so you should mention that. These things will determine which oscillatory mode is significant. $\endgroup$– GhosterCommented Jun 12, 2023 at 4:17
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$\begingroup$ I’m considering 2 options for how the bars will be supported: $\endgroup$– JpnolanCommented Jun 12, 2023 at 14:05
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$\begingroup$ First by hanging from the end, similar to wind chimes. Second option would be suspended horizontally similarly to marimba keys, using an elastic material or springs on either end. Sound to be produced by striking. Thanks for the help. $\endgroup$– JpnolanCommented Jun 12, 2023 at 14:09
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1 Answer
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You can use the resonant frequency formula for different overtones. So if you have a flute (or an open pipe) you can get the resonant frequency through $$f_n = \frac{nV}{2L}$$ where n is the number of overtone (1,2,3,4...), $V$ is the speed of sound in the medium and $L$ is the length of the tube
You can see the source for different resonant frequency of closed pipes and all. Source: https://www.texasgateway.org/resource/144-sound-interference-and-resonance
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$\begingroup$ The bars will not vibrate in the same way the air in a pipe will. Solids are way more complicated than air in their vibrations even in the linearised regime. They support bending, quasi-longitudinal as well as surface (transverse) waves. $\endgroup$– ZaellixACommented Jun 12, 2023 at 20:15
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$\begingroup$ @ZaellixA agreed but I think they meant to frequency coming from the instrument rather than the frequency at which the instrument will be resonating $\endgroup$ Commented Jun 13, 2023 at 9:30
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$\begingroup$ I don't understand... What do you mean with "the frequency coming from the instrument" and "not the frequency the instrument will be resonating"? The instrument will vibrate in certain frequencies of excitation with certain amplitude based on the material, geometry and boundary conditions of the instrument (and coupling if there's more "sub-systems"). This vibration will be radiated as sound. $\endgroup$– ZaellixACommented Jun 13, 2023 at 21:29
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$\begingroup$ @ZaellixA according to my knowledge it's not the vibration of the material that produces sound in the answer I've given but the air column forming standing waves that does. If it was some membrane instrument then it makes sense but not for open or closed flutes and instrument like that $\endgroup$ Commented Jun 14, 2023 at 5:43
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$\begingroup$ But the OP is about round bars not air columns inside some metal tube. To my understanding, this is about materials and more specifically bars. In this case the surface waves are the main radiating factor. $\endgroup$– ZaellixACommented Jun 14, 2023 at 14:08