The Vibrating String Considered as an Electrical Transmission Line

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Abstract
An analogy is drawn between the piano string and an electrical transmission line, utilizing a different correlation than is customary in usual electro-acoustical analogs. The current in the line is compared with the displacement and the voltage is compared with the momentum. With this correspondence the highly developed treatment of transmission lines becomes applicable to the piano string. The various cases discussed include: Open circuited line with and without attenuation (i.e., ideal and actual string with ends rigidly fixed), terminated line (string affixed to bridge of sound board), electrical impulse introduced (impact of piano hammer). A relation is derived giving the optimum position of striking point for a given ratio of hammer mass to string mass, and this is shown to agree with the results of George and Beckett. The appearance of the nth harmonic when the string is struck at 1/nth of its length is explained, likewise the advantages of the modern practice of high string tensions. Conclusions are drawn concerning impedance matching (string to soundboard) and the velocity of propagation for different frequencies.

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