Free-free bar: Difference between revisions
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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 '''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/ Hope Street Marimba | ''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 Mauro Caresta. ''Vibrations of a Free-Free Beam''. ]</ref> The ''n''-th [[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 HyperPhysics | ''Bar Resonances'']</ref> | ||
<math>f_n=0.441 | <math display="block">f_n = 0.441 \left( n + \frac{1}{2} \right) ^2 f_1</math> | ||
where < | where ''f''<sub>1</sub> is the fundamental frequency. | ||
== See also == | == See also == | ||
* [[Freave]] | * [[Freave]] | ||
== References == | == References == | ||
<references /> | <references /> | ||
{{Stub}} | |||
[[Category:Instruments]] | [[Category:Instruments]] | ||
[[Category:Math]] | [[Category:Math]] | ||
[[Category:Xenharmonic series]] | [[Category:Xenharmonic series]] | ||
Latest revision as of 11:57, 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 n-th overtone of a free bar can be approximately represented by the formula below.[3]
\begin{displaymjx}f_n = 0.441 \left( n + \frac{1}{2} \right) ^2 f_1\end{displaymjx}
where f1 is the fundamental frequency.
See also
References
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