Basic physics of xylophone and marimba bars
B. H. Suits
Abstract
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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