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Acoustics of the Marimba Heather Hill Advised by Professor Steven Errede Yamaha YM-5100A.

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Presentation on theme: "Acoustics of the Marimba Heather Hill Advised by Professor Steven Errede Yamaha YM-5100A."— Presentation transcript:

1 Acoustics of the Marimba Heather Hill Advised by Professor Steven Errede Yamaha YM-5100A

2 Striking Areas Center Off-Center Edge

3 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, (1995).

4 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

5 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

6 Exponential Time Decays for C 2

7 Exponential Time Decays for C n Bars

8 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

9 Average Eta Values for C n Bars

10 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 supports the REU program at UIUC.

11 Inharmonicity

12 Tuning Evolution

13 Resonator Effect on Harmonics


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