Acoustics of the marimba
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Acoustics of the Marimba. Heather Hill Advised by Professor Steven Errede. Yamaha YM-5100A. Striking Areas. Center Off-Center Edge. Frequency Ratios for Sculpted Marimba Bars. Bork’s Data 1. My Analysis.

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Acoustics of the Marimba

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Acoustics of the Marimba

Heather Hill

Advised by Professor Steven Errede

Yamaha YM-5100A


Striking Areas

  • Center

  • Off-Center

  • Edge


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).


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.


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.


Exponential Time Decays for C2


Exponential Time Decays for Cn Bars


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.


Average Eta Values for Cn Bars


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.


Inharmonicity


Tuning Evolution


Resonator Effect on Harmonics


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