The skewness of the first time derivative of a pressure waveform, or derivative skewness, has been used previously to describe the presence of shock-like content in jet and rocket noise. Despite its use, a quantitative understanding of derivative skewness values has been lacking. In this paper, the derivative skewness for nonlinearly propagating waves is investigated using analytical, numerical, and experimental methods. Analytical expressions for the derivative skewness of an initially sinusoidal plane wave are developed and, along with numerical data, are used to describe its behavior in the preshock, sawtooth, and old-age regions. Analyses of common measurement issues show that the derivative skewness is relatively sensitive to the effects of a smaller sampling rate, but less sensitive to the presence of additive noise. In addition, the derivative skewness of nonlinearly propagating noise is found to reach greater values over a shorter length scale relative to sinusoidal signals. A minimum sampling rate is recommended for sinusoidal signals to accurately estimate derivative skewness values up to five, which serves as an approximate threshold indicating significant shock formation.
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March 2016
March 28 2016
Evolution of the derivative skewness for nonlinearly propagating waves Available to Purchase
Brent O. Reichman;
Brent O. Reichman
a)
Department of Physics and Astronomy,
Brigham Young University
, N283 ESC, Provo, Utah 84602, USA
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Michael B. Muhlestein;
Michael B. Muhlestein
Department of Physics and Astronomy,
Brigham Young University
, N283 ESC, Provo, Utah 84602, USA
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Kent L. Gee;
Kent L. Gee
Department of Physics and Astronomy,
Brigham Young University
, N283 ESC, Provo, Utah 84602, USA
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Tracianne B. Neilsen;
Tracianne B. Neilsen
Department of Physics and Astronomy,
Brigham Young University
, N283 ESC, Provo, Utah 84602, USA
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Derek C. Thomas
Derek C. Thomas
Department of Physics and Astronomy,
Brigham Young University
, N283 ESC, Provo, Utah 84602, USA
Search for other works by this author on:
Brent O. Reichman
a)
Department of Physics and Astronomy,
Brigham Young University
, N283 ESC, Provo, Utah 84602, USA
Michael B. Muhlestein
Department of Physics and Astronomy,
Brigham Young University
, N283 ESC, Provo, Utah 84602, USA
Kent L. Gee
Department of Physics and Astronomy,
Brigham Young University
, N283 ESC, Provo, Utah 84602, USA
Tracianne B. Neilsen
Department of Physics and Astronomy,
Brigham Young University
, N283 ESC, Provo, Utah 84602, USA
Derek C. Thomas
Department of Physics and Astronomy,
Brigham Young University
, N283 ESC, Provo, Utah 84602, USA
a)
Electronic mail: [email protected]
J. Acoust. Soc. Am. 139, 1390–1403 (2016)
Article history
Received:
November 21 2014
Accepted:
February 29 2016
Citation
Brent O. Reichman, Michael B. Muhlestein, Kent L. Gee, Tracianne B. Neilsen, Derek C. Thomas; Evolution of the derivative skewness for nonlinearly propagating waves. J. Acoust. Soc. Am. 1 March 2016; 139 (3): 1390–1403. https://doi.org/10.1121/1.4944036
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