Free-free bar: Difference between revisions
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CompactStar (talk | contribs) Created page with "A '''free-free bar''' is an idealized bar that is completely free to vibrate at both ends without external constraints.<ref>http://www.hopestreetmarimba.com/a-driftwood-marimba-on-the-beach-of-improbability/</ref> A marimba or xylophone bar can be modeled by this. Free-free bars are highly inharmonic, and their vibration is governed by a complex differential equation which can be solved to determine the spectrum of a free bar <ref>https://web.archive..." |
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A '''free-free bar''' is an idealized bar that is completely free to vibrate at both ends without external constraints.<ref>http://www.hopestreetmarimba.com/a-driftwood-marimba-on-the-beach-of-improbability/</ref> A marimba or xylophone bar can be modeled by this. Free-free bars are highly [[harmonic timbre|inharmonic]], and their vibration is governed by a complex differential equation which can be solved to determine the spectrum of a free bar <ref>https://web.archive.org/web/20260816073448/http://www.varg.unsw.edu.au/Assets/link%20pdfs/Beam_vibration.pdf</ref>. The nth [[overtone]] of a free bar can be approximately represented by the formula below <ref>https://web.archive.org/web/20260212000442/http://hyperphysics.phy-astr.gsu.edu/hbase/Music/barres.html</ref> | A '''free-free bar''' is an idealized bar that is completely free to vibrate at both ends without external constraints.<ref>http://www.hopestreetmarimba.com/a-driftwood-marimba-on-the-beach-of-improbability/</ref> A marimba or xylophone bar can be modeled by this. Free-free bars are highly [[harmonic timbre|inharmonic]], and their vibration is governed by a complex differential equation which can be solved to determine the spectrum of a free bar <ref>https://web.archive.org/web/20260816073448/http://www.varg.unsw.edu.au/Assets/link%20pdfs/Beam_vibration.pdf</ref>. The nth [[overtone]] of a free bar can be approximately represented by the formula below<ref>https://web.archive.org/web/20260212000442/http://hyperphysics.phy-astr.gsu.edu/hbase/Music/barres.html</ref> | ||
<math>f_n=0.441[n+1\frac{1}{2}]^2f_1</math> | <math>f_n=0.441[n+1\frac{1}{2}]^2f_1</math> | ||
where <math>f_1</math> is the fundamental frequency. | where <math>f_1</math> is the fundamental frequency. | ||
Revision as of 01:26, 23 October 2026
A free-free bar is an idealized bar that is completely free to vibrate at both ends without external constraints.[1] A marimba or xylophone bar can be modeled by this. Free-free bars are highly inharmonic, and their vibration is governed by a complex differential equation which can be solved to determine the spectrum of a free bar [2]. The nth overtone of a free bar can be approximately represented by the formula below[3]
[math]\displaystyle{ f_n=0.441[n+1\frac{1}{2}]^2f_1 }[/math]
where [math]\displaystyle{ f_1 }[/math] is the fundamental frequency.
See also
References
- ↑ http://www.hopestreetmarimba.com/a-driftwood-marimba-on-the-beach-of-improbability/
- ↑ https://web.archive.org/web/20260816073448/http://www.varg.unsw.edu.au/Assets/link%20pdfs/Beam_vibration.pdf
- ↑ https://web.archive.org/web/20260212000442/http://hyperphysics.phy-astr.gsu.edu/hbase/Music/barres.html
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