Sauveur (1713)

Abstract

Joseph Sauveur presented his derivation of the vibrational frequency of a musical string to the Paris Académie Royale des Sciences in 1713. The paper was published¹ shortly after his death in 1716. In his derivation, Sauveur supposes that the string is stretched horizontally in a gravitational field and that it undergoes small horizontal vibrations. With the vibrations assumed small even compared with the sag in the string, Sauveur obtains the situation in which the string vibrates in a swinging motion. Somewhat implicitly he makes the simplifying assumption that the string undergoes this swinging motion as a rigid body. Thus he succeeds in reducing the problem to one that is already familiar. He emphasizes that in general the gravitational field has a negligible effect on a taut vibrating string and thus that his result for frequency holds in general.