ASA 125th Meeting Ottawa 1993 May

4pMU7. Root locus equations for the vibrating diaphragm model of jet-pipe action.

S. A. Elder

Phys. Dept., U.S. Naval Academy, Annapolis, MD 21402

The vibrating diaphragm model of jet-pipe action described in an earlier paper [S. A. Elder, J. Acoust. Soc. Am. 96, 2411 (A) (1992)] has been extended by the development of root locus equations for laminar and turbulent half-jet resonators, which allow solution for the shear wave propagation constant at resonance, and estimation of the oscillation amplitude. The ``force-drive'' term in the pipetone system is shown to be associated with the inertia of the separated shear layer, with power being delivered to sustain the oscillation whenever the inertial force has a component in phase with sound particle velocity in the pipe mouth. Turbulent boundary layers thus produce corresponding larger driving force, for the same frequency and jet speed, since they tend to be thicker and so possess larger inertia. [Work partially supported by U.S. Naval Academy Research Council.]