Measurements of sound output as a function of blowing pressure an reported
for a group of experienced trumpet players. The study identifies several co
mmon features, namely (1) a threshold blowing pressure approximately propor
tional to the frequency of the note being played, (2) an extended region in
which the sound output rises by about 15 dB for each doubling of blowing p
ressure, and (3) a saturation region in which sound output rises by only ab
out 3 dB for a doubling of blowing pressure. Some players are able to blow
with maximum pressures as high as 25 kPa, which is significantly greater th
an normal systolic blood pressure. A simple theory is presented that provid
es a physical explanation for the acoustical behavior, but a detailed treat
ment requires solution of the nonlinear coupled equations both for the lip-
valve mechanism and for nonlinear wave propagation in the instrument tube.
Frequency analysis of the sound shows a basic spectral envelope determined
by the resonance properties of the mouthpiece cup and the radiation behavio
r of the bell, supplemented by an extension to increasingly high frequencie
s as the blowing pressure is increased. This high-frequency behavior can be
attributed to nonlinear wavefront steepening during sound propagation alon
g the cylindrical bore of the instrument. (C) 1999 Acoustical Society of Am
erica. [S0001-4966(99)02102-5].