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
(Murray and Greated p. 431)

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.

 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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