Scaling the xylophone

The familiar xylophone produces musical sounds when its keys (a linear array of rectangular bars of dimensions axbxc, with progressively longer key lengths c producing lower audio frequencies) are struck by a mallet and go into transverse vibration perpendicular to the smallest, a, dimension. The traditional "middle C" in music corresponds to 256 Hz. If the size scale of the xylophone key is reduced to the micrometer scale, as has recently been achieved, using the semiconductor technology, and the mallet is replaced by electromagnetic excitation, the same transverse mechanical oscillations occur, and are measured to approach the Gigahertz (109Hz) range [5]!

The measured frequencies of the micrometer scale xylophone keys are still accurately described by the laws of classical physics. (Actually the oscillators that have been successfully miniaturized, see Figure 1.1, differ slightly from xylophone keys, in that they are clamped at both ends, rather than being loosely suspended. Very similar equations are known to apply in this case.) Oscillators whose frequencies approach the GHz range have completely different applications than those in the musical audio range!

Could such elements be used in new devices to replace Klystrons and Gunn oscillators, conventional sources of GHz radiation? If means could be found to fabricate "xylophone keys" scaling down from the micrometer range to the nanometer range, classical physics would presumably apply almost down to the molecular scale. The limiting vibration frequencies would be those of diatomic molecules, which lie in the range 1013 - 1014 Hz. For comparison, the frequency of light used in fiberoptic communication is about 2 x 1014 Hz.

Figure 1.1 Silicon nanowires in a harp-like array. Due to the clamping of the single-crystal silicon bars at each end, and the lack of applied tension, the situation is more like an array of xylophone keys. The resonant frequency of the wire of 2 micrometer length is about 400 MHz. After Reference [5]

Figure 1.1 Silicon nanowires in a harp-like array. Due to the clamping of the single-crystal silicon bars at each end, and the lack of applied tension, the situation is more like an array of xylophone keys. The resonant frequency of the wire of 2 micrometer length is about 400 MHz. After Reference [5]

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