Theoretical Investigation on End Correction Problems : Part III, Transient Properties of Open End

概要

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An open tube end does not necessarily realize an expected boundary of constant pressure for wave phenomena in a tube. Rayleigh has first formulated this fact for harmonic waves with a wave potential equation and a vibrating disc on a wall as a sound source, proposing his famous end correction theory. In contrast this paper theoretically sheds light on the 'transient' aspect of this problem to which little attention has been paid so far. The present study is started off with the same potential equation and a similar disc model which this time makes a sudden motion instead of vibration. The Laplace transformation proves to help make a successful transient wave analysis. Transitional behaviors of the pressure on and its average over the disc are mathematically determined. Subsequently the results are effectually applied to analytically estimating the true boundary condition of an open end for a transient wave.
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