Nonlinear Sound Propagation in Trumpets

The bright timbre of many brass instruments when played at loud dynamic levels is commonly characterised as "brassy". It is now widely acknowledged that this brassy quality to the sound is mainly due to nonlinear wave propagation along the instrument bore, which in turn results in a transfer of energy to high harmonics. Thus, longer instruments like the trombone might seem better suited to produce brassy sound than shorter ones like the trumpet, and observations of nonlinear propagation effects in trombones have, in fact, been reported. The length of the instrument bore is not, however, the sole factor that determines the scale of nonlinear propagation effects inside the instrument resonator – the shape of the instrument bore and the shape of the time signal at the mouthpiece are also important. Regarding the trumpet, there is some controversy as to the scale of spectral enrichment due to nonlinear wave propagation. With this in mind, we have measured both standing and progressive waves along the bore of a B trumpet. We have observed that for high enough dynamic levels, waveform steepening is quite noticeable in the time domain. By following progressive waves along the bore of the instrument, we have also been able to isolate the effect of nonlinearity from that of attenuation, and identify the transfer of energy to high frequencies that occurs as blowing pressure is increased. Using a live player, shock waves were detected at fortissimo levels, confirming that the scale of waveform steepening is sufficient to result in significant spectral enrichment of high frequencies.