A new calculational method is outlined for the eigenstates of internal rotors characterized by angle-dependent moments of inertia. The procedure is applied to the 1,3-butadiene molecule giving good agreement with transitions calculated by standard techniques. Independent checks are included to justify the numerical accuracy of the outlined procedure.

We report the observation of longitudinal vibrations in violin strings excited by bowing. These vibrations are detected from the rocking motion of the top of the bridge in the direction longitudinal to the strings, with the aid of a photoelectric device. The frequencies of these waves are approximately three octaves above the respective fundamental frequencies of the transverse string vibrations, in line with expectation. It is found that stable oscillations are difficult to sustain in which both the transverse and longitudinal motions can coexist in comparable strength. Essentially pure longitudinal oscillations can be excited by bowing at a forward angle. These modes are difficult to identify in the normal bowing spectrum, and are substantially absent in pizzicato tones, except in the initial transients.