Single-point characterization of spectral amplitude and phase changes due to nonlinear propagation

Brent Reichman; Kent L. Gee; Won Suk Ohm

doi:10.1121/2.0000870

Single-point characterization of spectral amplitude and phase changes due to nonlinear propagation

Brent Reichman, Kent L. Gee, Won Suk Ohm

Department of Mechanical Engineering

Research output: Contribution to journal › Conference article › peer-review

Abstract

A frequency-domain representation of the Burgers equation reveals that the cross-spectrum between the pressure and pressure-squared waveforms can be used to calculate nonlinear frequency-domain effects of finite-amplitude sound propagation. The normalized version of the quadspectrum, Q/S, was introduced by Morfey and Howell and has since been used to point to the nonlinear transfer of energy between frequencies, in particular gaining use in the domain of high-amplitude jet noise propagation. However, one question that remained was that of the interpretation: The physical meaning of the amplitude of Q/S was unclear. Recent analytical work has recast Q/S and the normalized version of the cospectrum, C/S, as a way to estimate sound pressure level and phase changes due to nonlinearity with a single-point measurement. This paper uses various measurements within a plane-wave tube to verify the physical significance of the amplitude and phase changes predicted by Q/S and C/S. Experiments involving sinusoids and band-passed Gaussian noise at various amplitudes show the validity of the single-point measurement to measure the strength of nonlinear effects in both amplitude and phase.

Original language	English
Article number	045018
Journal	Proceedings of Meetings on Acoustics
Volume	34
Issue number	1
DOIs	https://doi.org/10.1121/2.0000870
Publication status	Published - 2018
Event	21st International Symposium on Nonlinear Acoustics, ISNA 2018 - Santa Fe, United States Duration: 2018 Jul 9 → 2018 Jul 13

Bibliographical note

Funding Information:
The authors acknowledge Jared Oliphant for his help in conducting measurements. B.O. Reichman was funded through an appointment to the Student Research Participation Program at the U.S. Air Force Research Laboratory, 711th Human Performance Wing, Human Effectiveness Directorate, Warfighter Interface Division, Battlespace Acoustics Branch administered by the Oak Ridge Institute for Science and Education through an interagency agreement between the U.S. Department of Energy and USAFRL.

Publisher Copyright:
© 2018 Acoustical Society of America.

All Science Journal Classification (ASJC) codes

Acoustics and Ultrasonics

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10.1121/2.0000870

Cite this

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title = "Single-point characterization of spectral amplitude and phase changes due to nonlinear propagation",

abstract = "A frequency-domain representation of the Burgers equation reveals that the cross-spectrum between the pressure and pressure-squared waveforms can be used to calculate nonlinear frequency-domain effects of finite-amplitude sound propagation. The normalized version of the quadspectrum, Q/S, was introduced by Morfey and Howell and has since been used to point to the nonlinear transfer of energy between frequencies, in particular gaining use in the domain of high-amplitude jet noise propagation. However, one question that remained was that of the interpretation: The physical meaning of the amplitude of Q/S was unclear. Recent analytical work has recast Q/S and the normalized version of the cospectrum, C/S, as a way to estimate sound pressure level and phase changes due to nonlinearity with a single-point measurement. This paper uses various measurements within a plane-wave tube to verify the physical significance of the amplitude and phase changes predicted by Q/S and C/S. Experiments involving sinusoids and band-passed Gaussian noise at various amplitudes show the validity of the single-point measurement to measure the strength of nonlinear effects in both amplitude and phase.",

author = "Brent Reichman and Gee, {Kent L.} and Ohm, {Won Suk}",

note = "Funding Information: The authors acknowledge Jared Oliphant for his help in conducting measurements. B.O. Reichman was funded through an appointment to the Student Research Participation Program at the U.S. Air Force Research Laboratory, 711th Human Performance Wing, Human Effectiveness Directorate, Warfighter Interface Division, Battlespace Acoustics Branch administered by the Oak Ridge Institute for Science and Education through an interagency agreement between the U.S. Department of Energy and USAFRL. Publisher Copyright: {\textcopyright} 2018 Acoustical Society of America.; 21st International Symposium on Nonlinear Acoustics, ISNA 2018 ; Conference date: 09-07-2018 Through 13-07-2018",

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N2 - A frequency-domain representation of the Burgers equation reveals that the cross-spectrum between the pressure and pressure-squared waveforms can be used to calculate nonlinear frequency-domain effects of finite-amplitude sound propagation. The normalized version of the quadspectrum, Q/S, was introduced by Morfey and Howell and has since been used to point to the nonlinear transfer of energy between frequencies, in particular gaining use in the domain of high-amplitude jet noise propagation. However, one question that remained was that of the interpretation: The physical meaning of the amplitude of Q/S was unclear. Recent analytical work has recast Q/S and the normalized version of the cospectrum, C/S, as a way to estimate sound pressure level and phase changes due to nonlinearity with a single-point measurement. This paper uses various measurements within a plane-wave tube to verify the physical significance of the amplitude and phase changes predicted by Q/S and C/S. Experiments involving sinusoids and band-passed Gaussian noise at various amplitudes show the validity of the single-point measurement to measure the strength of nonlinear effects in both amplitude and phase.

AB - A frequency-domain representation of the Burgers equation reveals that the cross-spectrum between the pressure and pressure-squared waveforms can be used to calculate nonlinear frequency-domain effects of finite-amplitude sound propagation. The normalized version of the quadspectrum, Q/S, was introduced by Morfey and Howell and has since been used to point to the nonlinear transfer of energy between frequencies, in particular gaining use in the domain of high-amplitude jet noise propagation. However, one question that remained was that of the interpretation: The physical meaning of the amplitude of Q/S was unclear. Recent analytical work has recast Q/S and the normalized version of the cospectrum, C/S, as a way to estimate sound pressure level and phase changes due to nonlinearity with a single-point measurement. This paper uses various measurements within a plane-wave tube to verify the physical significance of the amplitude and phase changes predicted by Q/S and C/S. Experiments involving sinusoids and band-passed Gaussian noise at various amplitudes show the validity of the single-point measurement to measure the strength of nonlinear effects in both amplitude and phase.

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Single-point characterization of spectral amplitude and phase changes due to nonlinear propagation

Abstract

Bibliographical note

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