Spectral Enrichment of Transient Acoustic Waves as a Function of Input Signal Shape

Nonlinear acoustic propagation effects are known to account for waveform steepening for sufficiently intense signals having travelled over a long enough distance. This steepening, which will eventually produce a shock wave, results, in turn, in a transfer of energy to the high end of the frequency spectrum. The shock formation distance, however, is inversely proportional not to the maximum amplitude of the waveform, but to its maximum slope. We test this theoretical result by producing two sets of short pulses in a long cylindrical tube, where the energy content of each pulse in a set is constant, but the maximum slope varies. The pulses are allowed to propagate over a distance long enough for nonlinear steepening to become apparent. We observe the expected result, where for an initially loud signal the value of the maximum slope does affect the rate at which energy is pumped to high frequencies, whereas for a signal with much smaller initial energy content it does not. This result is of interest in the context of musical acoustics, as it confirms recent observations where players of some brass instruments can affect the brightness of their sound purely through slight changes in embouchure [16].