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Solid rods like you describe can be made to vibrate, but they are most resonant with compressive vibrations - hold the rod loosely at about a fourth of its length, and strike it on the end - it'll ring like a bell. Glue a thin disc of steel on the other end, and put that over a magnetic pickup. Only problem is, to get 4 notes, you'll need 4 different length rods. For bass notes, you'll need really long rods.
If you try to use rods like that with the movement being sideways (like a stringed instrument), you'll learn really fast why strings are wound, not solid. Solid rods have a lot of inherent stiffness - in flex, they're a dispersive medium, and the velocity of propagation is not constant with frequency. Practically speaking, that means the overtones of the vibration are not harmonics of the fundamental - the thing will sound out of tune with itself.
Really interesting physics problem. The distribution of harmonics on a vibrating string are caused by the boundary conditions, specifically that the string is fixed at both ends. The longitudinal waves reflect perfectly at the ends, the interference of all of this reflections produces the harmonic series. So if the rods are only supported/fixed on one end, they would resonate more like a tuning fork. You could probably look up the harmonic series and nodes/antinodes for a tuning fork, I would be surprised if that problem has not been solved.
I think these three are on to something. You're not likely to get predictable harmonic locations along the rods that you can clearly determine will produce a desired result. So you can find the fundamental, but hard to find usable, predictable harmonic overtones.This might be useful: Vibrational Modes of a Tuning Fork
This is very insightful, and describes to me why there is a "clang" component to the tone of percussions instruments like this: all the non-coherent (not in tune with the fundamental) overtones.Solid rods like you describe can be made to vibrate, but they are most resonant with compressive vibrations - hold the rod loosely at about a fourth of its length, and strike it on the end - it'll ring like a bell. Glue a thin disc of steel on the other end, and put that over a magnetic pickup. Only problem is, to get 4 notes, you'll need 4 different length rods. For bass notes, you'll need really long rods.
If you try to use rods like that with the movement being sideways (like a stringed instrument), you'll learn really fast why strings are wound, not solid. Solid rods have a lot of inherent stiffness - in flex, they're a dispersive medium, and the velocity of propagation is not constant with frequency. Practically speaking, that means the overtones of the vibration are not harmonics of the fundamental - the thing will sound out of tune with itself.
This is very insightful, and describes to me why there is a "clang" component to the tone of percussions instruments like this: all the non-coherent (not in tune with the fundamental) overtones.
If you look at a xylophone or marimba, you'll see the underside of each of the bars is not flat - it's cut away. That's because the same Physics is at work. By not having a uniform cross section, the overtones are closer to multiples of the fundamental - it sounds more in tune...
Yeah? I'd better get over there!If you check Talk Marimba right now, they're no doubt discussing teversed vs normal P pickup placement.