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
1Bork,
My Analysis
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
2.2
T 
 fn
n
60
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
2.2
ln10  n  T 
 fn
3
2Cremer,
n
60
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.
n


2


e Y   
m YE
E
2Cremer,

n n
Ing. L. and Heckl, rer. Nat. M. Körperschall, (Springer-Verlag, Berlin, 1967), pp. 165-201.
1
 n f n
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