Xylophone bars: Frequency and length

Here’s an additional note to M. Hurth et al’.s excellent article, “Harmonic Resonances in Metal Rods – Easy Experimentation with a Smartphone and Tablet PC” in the March 2016 issue of TPT. For a xylophone, such as shown in Fig. 1 (their Fig. 8) with the bars clamped in two specific positions, the dependence of the frequencies f of the musical pitches produced by the vibrations of the bars on their lengths L when struck is f ∼ 1/L². Figure 2 is a typical student plot showing this dependence from an experiment done in HFC’s Sound & Light in Fine Arts class using a xylophone identical to that shown in Fig. 1. The vibration frequencies of the bars could be verified by measurement with a smartphone or tablet but, as can be seen in Fig. 1, they are also written on the base of...