Acoustics of the Marimba Heather Hill Advised by Professor Steven Errede Yamaha YM-5100A
Dec 31, 2015
Acoustics of the MarimbaHeather 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
T60n
2.2
fn
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
ln103 n T60n
2.2
fn
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.
2 1E
nn n n nE
m Y
fe Y
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 τn
are 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