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Understanding the physical principals of vibrating bars with two free ends, one must then be able calculate the fundamental frequency of a vibrating bar in order to construct the definitely pitched bars of the marimba. This can be found through the following equation:
f = 1.03 ( t ( Y / p )^0.5 ) / L^2
In this equation, L represents the length of the bar, t represents its thickness, and both Y and p, representing Young's modulus and density (respectively), are dictated by the material used to make the bar. Figure 3 shows some values of Young's modulus and density for a few types of wood often used in the construction of bars for mallet instruments.
(Murray and Greated p. 431)
| Material | Young's modulus (Nm^-2) | Density (kgm^-3) |
| Brazilian Rosewood | 1.6 x 10^10 | 830 |
| Indian Rosewood | 1.2 x 10^10 | 740 |
| African Mahogany | 1.2 x 10^10 | 550 |
| European Maple | 1.0 x 10^10 | 640 |
| Redwood | 0.95 x 10^10 | 380 |
| Sitka Spruce | 1.3 x 10^10 | 470 |
Figure 3: Density and Young's modulus for several types of wood
(Fletcher and Rossing, p.534)
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