Blowing pressure, power, and spectrum in trumpet playing

Measurements of sound output as a function of blowing pressure are reported for a group of experienced trumpet players. The study identifies several common features, namely (1) a threshold blowing pressure approximately proportional 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 pressure, and (3) a saturation region in which sound output rises by only about 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 than normal systolic blood pressure. A simple theory is presented that provides a physical explanation for the acoustical behavior, but a detailed treatment 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 behavior of the bell, supplemented by an extension to increasingly high frequencies as the blowing pressure is increased. This high-frequency behavior can be attributed to nonlinear wavefront steepening during sound propagation along the cylindrical bore of the instrument.