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Vibrations Are Limitless, Behavior Is Not
A guitar string exemplifies that while there are infinite potential shapes and vibrations, the behavior of the string when plucked naturally falls into a discrete set of harmonic frequencies. This means that even though the string itself isn't constrained, its most efficient modes of vibration, or harmonics, emerge from physical constraints at both ends. Hence, the discreteness observed in harmonics arises from specific patterns of vibration rather than the intrinsic limitations of the string.