Blowing pressure, power, and spectrum in trumpet playing

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].