Theory of Organ Pipe Sound Generation Free

By calculating force per unit area exerted by jet on a control volume extending from languid to edge and equating this to difference in acoustic pressure along pipe axis over this region, it is possible to derive an expression for acoustic particle velocity in the standing wave as a function of jet driving flow spectrum. The latter is proportional to initial jet speed and is further determined by fraction of time spent by jet below edge during each cycle, and phase of jet displacement upon arrival at edge. Over‐all feedback loop can be closed by introducing superposed Rayleigh‐Cremer type jet waves and finding solutions that give self‐consistent asymmetry factor and phase of jet displacement fundamental. Interaction of partials occurs both in driving mechanism and in nonlinear mouth impedance. At least four nonlinear mechanisms are present in the process. Using a variational method, computer solutions are being obtained out to third harmonic. Theory predicts approximately equal acoustic volume flow out of both ends of pipe, explaining Coltman's result. Momentum conservation requires entrainment coefficient of approximately (2Q/πc) in agreement with slope of empirical entrained‐flow curve of Cremer and Ising. [This work was supported by the Office of Naval Research.]