Two complex effective lengths for musical wind instruments
R. Dean Ayers · The Journal of the Acoustical Society of America · 1995
The definition of effective length has been generalized to all frequencies by Pyle, working in the context of lossless plane-wave horn theory [R. W. Pyle, Jr., J. Acoust. Soc. Am. 57, 1309–1317 (1975)]. In this paper, losses due to radiation and visco-thermal damping are included by letting the effective length become complex. With that additional generalization, effective length, pressure reflection coefficient, and relative input impedance carry exactly equivalent information. There are two choices of boundary condition at the downstream end of an idealized, uniform pipe: open or closed. The effective length to a closed end was used implicitly by Pyle, and a practical application for it is found in a doubly closed pipe model for the brass wind instruments.