Nonlinear interactions in organ flue pipes

The ideas introduced by Coltman and Benade are developed into a quantitative formalism for treating the oscillatory behavior of an air column in nonlinear interaction with an air jet, as in an organ flue pipe or a flute. Explicit solutions are given for the case when the pipe has only two resonances and the nonlinearity is described up to cubic terms. The results of illustrative calculations are discussed.