On the vibrations of an N-string

We study the small-amplitude transverse oscillations of a planar network of N sections of string which are all attached at one common extremity. This network is called an N-string. When the N sections of string are of finite length, we find Fourier series expressions describing the vibrations perpen dicular to the plane containing the N-string at rest. The standing perpendi cular wave energies of a plucked symmetric N-string are analyzed. It is fou nd that higher harmonics can be excited to an energy level above that of th e first harmonic simply by plucking at an appropriate location along one of the strings. This result is in contrast to an ordinary plucked string and may lead to interesting applications; most notably the construction of new musical instruments. We also describe the movements of one travelling perpe ndicular wave in an N-string as well as the interaction of such waves. A me thod for increasing or reducing the amplitude of travelling perpendicular w aves is outlined. (C) 2000 Academic Press.