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