The effects of the flaring bell on the normal frequencies of a trombone

Abstract

As sinusoidal waves encounter the bell of a brass wind instrument, they are effectively reflected by the flaring part of the bore. A given frequency is effectively reflected from that part of the bell where a significant change in bore radius occurs within a wavelength. Hence the longer wavelengths reflect from points closer to the inlet end of the bell than do the shorter wavelengths. A computer calculation of the equivalent lengths corresponding to the normal frequencies shows this effect, and shows how the frequency shifts depend on the shape of the bore. Through this effect, the bell makes an important contribution towards making the normal frequencies harmonic.