LIII.On the Helmholtz theories of the struck string.—Part I.Theoretical

Abstract

Summary The various theoretical treatments of the struck string are noted, and the Helmholtz theory for the hard hammer is then considered in detail, and is shown to be in conflict with experimental evidence. The Helmholtz theory for the elastic hammer is next considered, with the omission of two assumptions which caused Kaufmann to reject the theory. Expressions are found for quantities whose magnitude can be determined from photographically obtained displacement-time curves of the struck point. Expressions for the same quantities are derived from Kaufmann's theory of the string struck at the mid-point, and also from Kaufmann's approximate theory of the string struck near one end. The comparison of the theoretically and experimentally determined quantities is to be given in the second part of the paper.