Below are hyperlinks to waveforms that supplement a paper published in the AIAA Journal.

"On the Perception of Crackle in High-Amplitude Jet Noise"

(Published in AIAA Journal, Vol. 45, March 2007)

K. L. Gee

Department of Physics and Astronomy

Brigham Young University

Provo, UT 84602


V. W. Sparrow, A. A. Atchley, and T. B. Gabrielson

Graduate Program in Acoustics

The Pennsylvania State University

University Park, PA 16802


Article Synopsis and Waveform Descriptions


The article explores the suitability of skewness as a quantifier of the subjective phenomenon of crackle that is often present in supersonic jet noise.  The skewness is the third central moment of the probability density function ((PDF) of the time series data.  Ffowcs Williams et al. [J. Fluid Mech. 71, 251-271 (1975)] first explored the phenomenon of crackle and concluded that waveforms with skewness greater than 0.3 crackled and those with smaller skewness did not.  In this investigation, this finding was tested by using non-Gaussian simulation theory to create highly skewed waveforms that had virtually identical PDFs and power spectra as actual jet noise waveforms.

The first waveform shown below (Gaussian Waveform) is a Gaussian noise waveform with the same spectral shape as a jet aircraft at afterburner.  The second waveform (Non-Gaussian Simulation) is a skewed waveform that was created by nonlinearly transforming the Gaussian waveform.  The skewness of the non-Gaussian simulation is 0.57.  According to Ffowcs Williams et al., crackle should readily perceptible in the waveform, but it is not.  The reasons for this are explored in the article.  Both waveforms below are 16-bit mono .WAV files, sampled at 44.1 kHz.

Gaussian Waveform

Non-Gaussian Simulation