Yulia J. Benson
Sergey N. Makarov
Math. and Mech. Dept., State St. Petersburg Univ., 2 Bibliotechnaya Pl., St. Petersburg 198904, Russia
The aim of the present work is to demonstrate a principally new approach to the problem of the definition of the boundary condition at the open end of the tube when the incoming wave is a pure sine with frequency corresponding to the first linear resonance and the outcoming wave is unknown. An account of interaction of those two oppositely directed waves leads to the modified Burgers' equation for the initial sound wave. The method proposed allows one to describe the latter wave by the same equation. The numerical analysis of this equation by Adams' method and predictor-corrector scheme permits one to calculate the unknown outcoming wave and to define the boundary condition at the open end as a superposition of the incoming and outcoming waves. It is shown that results obtained are in good agreement with those predicted by the Sturtevant's experiment [B. Sturtevant, J. Fluid Mech. 63(1), 97--120 (1974)].