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Acoustics of the Marimba Heather 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 Data 1 My Analysis 1 Bork, 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 2 Cremer, 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 2 Cremer, Ing. L. and Heckl, rer. Nat. M. Körperschall, (Springer-Verlag, Berlin, 1967), pp. 165-201.

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Exponential Time Decays for C 2

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Exponential Time Decays for C n Bars

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Calculating Eta Using Cremer’s Equation, 2 I solved for η. 2 Cremer, Ing. L. and Heckl, rer. Nat. M. Körperschall, (Springer-Verlag, Berlin, 1967), pp. 165-201.

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Average Eta Values for C n Bars

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Summary The harmonics present in a sculpted marimba bar are f 1, f 4, f 10, and f 20. The exponential time decay constants τ n are inversely proportional to the frequency The mean absorptivity of rosewood is = 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

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The cross products are equal, so the ratios are in proportion.

The cross products are equal, so the ratios are in proportion.

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