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The intensity of sound waves can be related to displacement and pressure amplitudes by using their wave expressions and the definition of intensity. The critical step to achieve this is to write the power delivered by the particles on the wave as the product of force and velocity and simplify the force per unit area as the pressure. The velocity of the medium's particles can be derived from the displacement.
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Consider two sources of sound, that may or may not be in phase, emitting waves at a single frequency, and consider the frequencies to be the same.
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A coherence-based phase and amplitude gradient estimator method for calculating active acoustic intensity.

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The coherence-based phase and amplitude gradient estimator (CPAGE) method improves acoustic intensity calculations by addressing noise contamination. This advanced technique enhances both the magnitude and direction accuracy of intensity estimates, outperforming traditional methods.

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Area of Science:

  • Acoustics
  • Signal Processing
  • Noise Analysis

Background:

  • Traditional p-p methods for acoustic intensity calculation have limitations, especially with broadband sources.
  • The phase and amplitude gradient estimator (PAGE) method offers improvements but is susceptible to noise.
  • Noise contamination degrades accuracy and reduces coherence in microphone probe pairs for both methods.

Purpose of the Study:

  • To introduce and evaluate the coherence-based phase and amplitude gradient estimator (CPAGE) method.
  • To mitigate the impact of noise on acoustic intensity calculations.
  • To improve the accuracy of both the magnitude and direction of acoustic intensity estimates.

Main Methods:

  • Developed the coherence-based phase and amplitude gradient estimator (CPAGE) method.
  • Implemented two key adjustments: pressure magnitude adjustment and phase gradient adjustment, both leveraging coherence.
  • The pressure magnitude adjustment mitigates uncorrelated noise effects on intensity magnitude.
  • The phase gradient adjustment uses coherence weighting for improved intensity direction calculation.

Main Results:

  • The CPAGE method demonstrates enhanced accuracy in acoustic intensity calculations compared to the PAGE method.
  • The pressure magnitude adjustment effectively reduces noise impact on intensity magnitude.
  • The phase gradient adjustment significantly improves the accuracy of intensity direction estimation, especially at low coherence.

Conclusions:

  • The CPAGE method provides more accurate acoustic intensity estimates, particularly in the presence of noise.
  • Coherence-based adjustments are crucial for improving intensity magnitude and direction calculations.
  • Despite increased computation time, CPAGE offers superior performance for energy-based acoustic measures.