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

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.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 ...