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Effective Gol'dberg number for diverging waves.

Mark F Hamilton1

  • 1Applied Research Laboratories, The University of Texas at Austin, Austin, Texas 78713-8029, USA.

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Summary
This summary is machine-generated.

A new effective Gol'dberg number quantifies nonlinear distortion in diverging waves. This number accurately predicts waveform distortion, similar to plane waves, for various wave types like spherical and cylindrical waves.

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Area of Science:

  • Acoustics
  • Nonlinear Wave Phenomena
  • Fluid Dynamics

Background:

  • Nonlinear distortion is a critical factor in wave propagation.
  • Quantifying nonlinear distortion in diverging waves presents unique challenges.
  • Existing metrics are often insufficient for complex wave geometries.

Purpose of the Study:

  • To propose an effective Gol'dberg number for quantifying nonlinear distortion in diverging wave fields.
  • To establish a metric applicable to various diverging wave types.
  • To provide a tool for predicting waveform distortion in realistic acoustic scenarios.

Main Methods:

  • Development of a theoretical framework for an effective Gol'dberg number.
  • Mathematical derivation of expressions for spherical waves, cylindrical waves, Gaussian beams, and exponential horns.
  • Comparison with traditional Gol'dberg number for plane waves.

Main Results:

  • An effective Gol'dberg number is proposed and defined.
  • For large values, this number correlates strongly with the degree of nonlinear waveform distortion.
  • The proposed metric shows comparable accuracy to the traditional Gol'dberg number for plane waves.

Conclusions:

  • The effective Gol'dberg number provides a robust measure of nonlinear distortion in diverging waves.
  • This metric simplifies the analysis of nonlinear acoustics in various geometries.
  • The proposed number is valuable for predicting wave behavior in applications involving diverging sound fields.