Recent research has indicated that broadband noise waveforms that propagate nonlinearly are perceived differently than those that propagate according to linear theory.  This research is the subject of an Express Letter published in the Journal of the Acoustical Society of America.  Below are each of waveforms that have been embedded as part of the letter, as well as accompanying explanation.  A further publication examined the use of time-varying loudness to quantify the  perceptual differences in shock-containing signals.  We have postulated that nonlinearity present in legacy low-bypass commercial aircraft noise may have been responsible for aircraft noise being deemed more annoying than other forms of transportation.



Input Waveform

The following waveform is a shaped broadband noise spectrum with a 6 dB/octave slope below the peak frequency of approximately 100 Hz and a -6 dB/octave slope above the peak frequency in order to simulate a jet mixing noise spectrum.  For the purposes of numerical propagation, the waveform was scaled to have an overall sound pressure level of 150 dB re 20 µPa at 10 m.  This and the other waveforms are 16-bit .wav files sampled at 44.1 kHz.



Linearly Propagated Waveform

The input waveform was numerically propagated to a distance of 1 km with spherical spreading and atmospheric absorption and dispersion.  In order to hear the input and the propagated waveforms at the same audio playback level, the effect of spherical spreading has been removed from the predicted waveforms by multiplying the propagated waveform by a factor of 100.



Nonlinearly Propagated Waveform

This waveform is the result of propagating the input waveform out to 1 km with a numerical model that solves the generalized Burgers equation for spherical spreading and atmospheric absorption and dispersion.  The generalized Burgers equation is a parabolic (one-way) model equation that describes finite-amplitude propagation in the far-field of the source.




Despite the fact that informal listening tests have indicated that there is a clear perceptual difference between the nonlinearly and linearly propagated waveforms, standard single-number metrics (such as A-weighted sound pressure level, Mark-VII perceived loudness, or Zwicker loudness) appear to fail in revealing that difference.  The question of the perceptual impact of nonlinearly propagated noise is the subject of ongoing research.

For more information regarding this research, contact Kent Gee (