Parabolic curves in a Helmholtz solution for a bowed string

Gómez, J.B. (Universidad de Zaragoza) ; Brun, J.L.

Resumen: If one is not familiar with the physics of the violin, it is not easy to guess, even for an experimental physicist, that the so-called Helmholtz motion can be obtained as a solution to the one-dimensional wave equation for the motion of a bowed violin string. It is worth visualising this aspect from a graphical perspective without recourse to ordinary Fourier analysis, as has customarily been done. We show in this paper how to obtain the shape of the Helmholtz trajectory, that is, two mirror-symmetric parabolas, in the ideal case of no losses from internal dissipation and no viscous drag from the air and the non-rigid end supports. We also show that the velocity profile of the Helmholtz motion is also a solution of the one-dimensional wave equation. Finally, we again derive the parabolic shape of the Helmholtz trajectory by applying the principle of energy conservation to a violin string.

Idioma: Inglés

DOI: 10.1088/1361-6404/aae8b5

Año: 2019

Publicado en: EUROPEAN JOURNAL OF PHYSICS 40, 1 (2019), 015802 [13 pp]
ISSN: 0143-0807

Factor impacto JCR: 0.756 (2019)

Categ. JCR: PHYSICS, MULTIDISCIPLINARY rank: 69 / 85 = 0.812 (2019) - Q4 - T3
Categ. JCR: EDUCATION, SCIENTIFIC DISCIPLINES rank: 36 / 41 = 0.878 (2019) - Q4 - T3

Factor impacto SCIMAGO: 0.437 - Physics and Astronomy (miscellaneous) (Q2)

Tipo y forma: Article (Published version)

Área (Departamento): Área Petrología y Geoquímica (Dpto. Ciencias de la Tierra)