The Departure of the Overtones of a Vibrating String from a True Harmonic Series
Robert S. Shankland · The Journal of the Acoustical Society of America · 1938
The changes in frequency caused by variations in tension due to the amplitude of vibration of a wire are treated by the method of perturbations. The constraints introduced by the bridges at the end nodes as studied by Raman, and on the bending moments due to the stiffness of the wire are included in the treatment. The overtones do not, in general, form a true harmonic series. In general, the combined influence of stiffness and amplitude sharpens the overtones with respect to the fundamental. A new type of monochord has been designed with which a cathode ray oscillograph is used to determine the effect of amplitude on frequency of strings of various lengths, diameters and materials. The absolute frequency is determined with a thyratron scale-of-sixteen circuit in connection with a Riesler standard clock. The electrically maintained vibrations are essentially free vibrations corresponding to the vibrations of piano wires. The degree of departure to be expected from an exact harmonic series for these instruments is shown to be in agreement with the studies by Miller for piano wires.