Effective length of horns
Robert W. Pyle · The Journal of the Acoustical Society of America · 1975
Some authors writing about brass musical instruments have used the term ’’effective length,’’ usually meaning the length of a cylindrical tube having the same resonance frequencies as a given horn, but possibly with different end conditions. In this paper, alternative definitions of effective length are considered, and one definition is chosen and generalized to all frequencies, not just discrete resonance frequencies. Within the framework of lossless plane-wave horn theory, a nonlinear first-order differential equation is derived that yields effective length as a function of frequency and horn contour. Effective length has been calculated for some horn contours resembling French horns and trumpets. The solutions are qualitatively consistent with the experience of instrument makers and players, and with the effective lengths of actual instruments, determined from measured resonance frequencies. Subject Classification: 85.60; 75.40.