Basic physics of xylophone and marimba bars

B. H. Suits
The frequency-dependent wave velocity and nonsinusoidal spatial dependence found for transverse waves in finite vibrating bars stands in stark contrast to the solutions to the one-dimensional wave equation, for example for the idealized vibrating string. The difference is particularly important when the resulting vibrations are used to produce music. Here, the appropriate approximate equations for transverse vibrations on a uniform bar are developed and compared to measurements using wooden bars. The results are extended using a simple finite element model to provide a means to predict normal mode behavior in nonuniform wooden bars such as those used for xylophones, marimbas, and related musical instruments.

American Journal of Physics 69, 743-750 (2001).

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