Why Are Marimba Bars Carved into an Arch Underneath?

From above, the bars of a marimba look like neat, flat pieces of wood. Turn one over and its centre has been carved into an arch. This is neither decoration nor simply a way to reduce weight: it is part of the tuning process.

When struck, a wooden bar does not vibrate at only one frequency. It produces a fundamental and several higher modes, and both pitch and tone colour depend on their relationship. If pitch were controlled only by shortening a bar to raise it or lengthening it to lower it, bass notes would require extremely long pieces of wood. By removing small amounts of material from particular places underneath, a maker can lower selected vibration modes, with the central region being especially influential on the fundamental. The arch therefore allows a bar of manageable length to reach its target pitch while its important overtones are adjusted.

A marimba and a xylophone do not sound the same even when both play the same C. Yamaha's instrument guide explains that marimba bars are tuned so that the fundamental and selected higher partials form a particular relationship, while xylophone tuning emphasises a different pattern. What matters to the listener is not a single generic “wooden” sound, but the way the clear attack, warm body and brief decay combine into one note. The hidden curve under the bar is arranging those proportions inside the sound.

https://www.yamaha.com/en/musical_instrument_guide/marimba/structure/
https://www.yamaha.com/en/musical_instrument_guide/marimba/structure/structure003.html