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 perpendicular to the plane containing the N -string at rest. The standing perpendicular wave energies of a plucked symmetric N -string are analyzed. It is found that higher harmonics can be excited to an energy level above that of the 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 perpendicular wave in an N -string as well as the interaction of such waves. A method for increasing or reducing the amplitude of travelling perpendicular waves is outlined.