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Acoustics of the Marimba

Acoustics of the Marimba

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Acoustics of the Marimba

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  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 Data1 My Analysis 1Bork, Ingolf. “Practical Tuning of Xylophone Bars and Resonators,” Appl. Acoust. J. Acoust. 46, 103-127 (1995).

  4. Frequency and Time Decay The reverberation time for each harmonic is inversely proportional to the frequency.2 2Cremer, Ing. L. and Heckl, rer. Nat. M. Körperschall, (Springer-Verlag, Berlin, 1967), pp. 165-201.

  5. Frequency and Time Decay The reverberation time for each harmonic is inversely proportional to the frequency.2 2Cremer, Ing. L. and Heckl, rer. Nat. M. Körperschall, (Springer-Verlag, Berlin, 1967), pp. 165-201.

  6. Exponential Time Decays for C2

  7. Exponential Time Decays for Cn Bars

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

  9. Average Eta Values for Cn Bars

  10. Summary • The harmonics present in a sculpted marimba bar are f1, f4, f10, and f20. • The exponential time decay constants τnare 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.

  11. Inharmonicity

  12. Tuning Evolution

  13. Resonator Effect on Harmonics