Acoustics of the Marimba
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Acoustics of the MarimbaHeather Hill
Advised by Professor Steven Errede
Yamaha YM-5100A
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Striking Areas
• Center
• Off-Center
• Edge
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Frequency Ratios for Sculpted Marimba Bars
Bork’s Data1 My Analysis
1Bork, Ingolf. “Practical Tuning of Xylophone Bars and Resonators,” Appl. Acoust. J. Acoust. 46, 103-127 (1995).
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Frequency and Time Decay
The reverberation time for each harmonic is inversely proportional to
the frequency.2
T60n
2.2
fn
2Cremer, Ing. L. and Heckl, rer. Nat. M. Körperschall, (Springer-Verlag, Berlin, 1967), pp. 165-201.
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Frequency and Time Decay
The reverberation time for each harmonic is inversely proportional to
the frequency.2
ln103 n T60n
2.2
fn
2Cremer, Ing. L. and Heckl, rer. Nat. M. Körperschall, (Springer-Verlag, Berlin, 1967), pp. 165-201.
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Exponential Time Decays for C2
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Exponential Time Decays for Cn
Bars
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Calculating Eta
Using Cremer’s Equation,2 I solved for η.
2 1E
nn n n nE
m Y
fe Y
2Cremer, Ing. L. and Heckl, rer. Nat. M. Körperschall, (Springer-Verlag, Berlin, 1967), pp. 165-201.
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Average Eta Values for Cn
Bars
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Summary• The harmonics present in a sculpted
marimba bar are f1, f4, f10, and f20. • The exponential time decay constants τn
are inversely proportional to the frequency• The mean absorptivity of rosewood is
<η> = 0.45% ± 0.09%• The methodology we have developed can
be used to analyze the decay times of other musical instruments, room acoustics, etc.
Acknowledgements: I thank Professor Steven Errede for a wonderful summer and for all of his
advice and support. I also thank John Nichols for his additional guidance.
The NSF Grant PHY-1062690 supports the REU program at UIUC.
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Inharmonicity
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Tuning Evolution
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Resonator Effect on Harmonics