Explosive Acoustics

Crackle is a phenomenon sometimes found in supersonic jet noise and can comprise an annoying and dominant part of the overall perceived noise. In the past, crackle has been commonly quantified by the skewness of the time waveform. In this investigation, a simulated waveform with a virtually identical probability density function and power spectrum as an actual F/A-18E afterburner recording has been created by nonlinearly transforming a statistically Gaussian waveform. Although the afterburner waveform crackles noticeably, playback of the non-Gaussian simulated waveform yields no perception of crackle at all, despite its relatively high skewness. Closer examination of the two waveforms reveals that although they have virtually identical statistics, there are considerable differences in their time rates of change in the intense compressive portions of the waveforms. The afterburner waveform is much more shocklike with its more rapid variations in pressure than the non-Gaussian simulated waveform. This results in a significant difference in the probability distributions of the time derivatives of the actual and simulated data and suggests that the perception of crackle in jet noise waveforms may be better quantified with statistics of the time derivative of the waveform, rather than by the skewness of the time waveform itself.

The use of conventional metrics to quantify the perception of nonlinearly propagated noise has been studied. Gaussian noise waveforms have been numerically propagated both linearly and nonlinearly, and from the resulting waveforms, several metrics are calculated. These metrics are overall, A-, C-, and D-weighted sound pressure levels, perceived noise level, Stevens Mark VII perceived loudness, Zwicker loudness, and sharpness. Informal listening demonstrations indicate that perceived differences in annoyance between linearly and nonlinearly propagated waveforms are substantial. Because the metrics studied seem inadequate in representing the perceived differences, rigorous subjective testing is encouraged to properly quantify and understand these differences. (c) 2007 Acoustical Society of America.

Far field propagation measurements of high-amplitude periodic signals generated by the U. S. Army Research Laboratory's Mobile Acoustic Source (MOAS) have been made. The MOAS is a large horn-coupled electropneumatic loudspeaker capable of producing sound at a few hundred hertz with a maximum overall sound pressure level of 155 dB re 20 mu Pa at 1 m. The possible influence of nonlinear effects have been investigated because the measurements exhibit greater sound pressure levels at high harmonics than are predicted by a linear propagation model. Between 100 and 375 m, nonlinearly predicted spectra obtained via a generalized Burgers equation-based model are consistently closer to measured spectra than are linear predictions, according to calculations of mean absolute error. These comparisons strengthen the assertion that nonlinearity is, in fact, the primary cause of disagreement between the measured and linearly predicted spectra at high frequencies. Comparisons between the nonlinear model and measurements, however, yield increased errors for greater propagation distances (similar to 1 km) and for measurements made later in the afternoon. For these cases, the nonlinear model calculations generally predict greater sound pressure levels at high frequencies than are actually present in the MOAS measurements. Despite the increased errors for these latter comparisons, the nonlinear model still typically performs better than the linear model. This provides additional confirmation of the presence of nonlinearity in the propagation, but may also point to the need to account for atmospheric variability in the numerical model to provide improved predictions. (c) 2006 Acoustical Society of America.

There is evidence to suggest that nonlinearity is important in the propagation of high-amplitude jet noise [Gee et al., AIAA J. 43(6), 1398-1401 (2005)]. Typically, the power spectral density (PSD) is used to assess the impact of jet noise on the surrounding environment, but such an assessment requires multiple measurement locations to observe the nonlinear evolution of the PSD. The difference in the PSDs measured at different locations depends on a combination of source level, nozzle diameter, and propagation distance. As a result, full scale measurements have to be extended over large distances, and model scale measurements require high measurement bandwidths. These constraints complicate the measurement and make it difficult to observe nonlinear effects using the PSD. Here a different technique for determining the importance of nonlinearity is investigated. The imaginary part of the cross-spectral density of the pressure and the square of the pressure, also called the quadspectral density (QSD), is related to the rate of nonlinear change of the PSD. Thus, the extent to which the PSD is evolving nonlinearly can be determined at a single measurement location. In the absence of absorption, energy is conserved, and the integration of the product of the QSD with frequency over all frequencies must be zero; when nonlinearity is present, the value of the QSD can be nonzero for many frequencies. Because nonlinearity tends to transfer energy from low frequencies to high frequencies and the QSD is positive at frequency components that are losing energy, using the integral of the QSD over its positive values as a nonlinearity indicator eliminates the need for high bandwidth measurements. Experimental measurements were taken in a plane wave tube with a working length of 9.55 m in which boundary layer losses dominate over atmospheric absorption. Experimental and numerical results show that the ratio of the integral of the QSD over the frequencies for which it is positive (Qpos) to the integral over the frequencies for which it is negative (Qneg) is close to one. Also, because the QSD is third order in pressure, normalizing its integral by the cube of the rms pressure yields a quantity that is easily compared across experimental conditions. Results for both periodic and broadband signals are presented and the practicality of using the QSD as a single-point indicator of nonlinearity addressed.

Crackle is a phenomenon sometimes found in supersonic jet noise. It has been commonly quantified by the skewness of the time waveform. In this investigation, a simulated waveform with a virtually identical probability density function and power spectrum as an actual F/A-18E afterburner recording has been created by nonlinearly transforming a statistically Gaussian waveform. Although the afterburner waveform crackles noticeably, playback of the non-Gaussian simulated waveform yields no perception of crackle at all, despite its relatively high skewness. Closer examination of the two waveforms reveals that although they have virtually identical statistics, there are considerable differences in their time rates of change in the intense compressive portions of the waveforms. The afterburner waveform is much more shock-like with its more rapid variations in pressure that the non-Gaussian simulated waveform. This results in a significant difference in the probability distributions of the time derivatives of the actual and simulated data and suggests that the perception of crackle in jet noise waveforms may be better quantified with statistics of the time derivative of the waveform, rather than by the skewness of the time waveform itself.