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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

Acoustics of the Marimba

Heather Hill

Advised by Professor Steven Errede

Yamaha YM-5100A


Striking areas
Striking Areas

  • Center

  • Off-Center

  • Edge


Frequency ratios for sculpted marimba bars
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
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 decay1
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.




Calculating eta
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.



Summary
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.





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