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This study numerically constructs the Green's function (GF) using geometric ray tracing for wave equations. The method accurately models sound fields and acoustic modes, showing potential for low-frequency acoustics.

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Area of Science:

  • Computational physics
  • Acoustics modeling

Background:

  • The Green's function (GF) is crucial for solving wave equations.
  • Geometric acoustics methods traditionally struggle with low-frequency phenomena.

Purpose of the Study:

  • To numerically construct the Green's function (GF) for the scalar wave equation.
  • To apply and validate this method in acoustic modeling, particularly for rectangular rooms.

Main Methods:

  • Employs an advanced geometric ray-tracing method based on the eikonal approximation.
  • Implements a ray-tracing numerical simulation for acoustic field calculation.
  • Calculates acoustic modes within a rectangular room.

Main Results:

  • Successfully simulates the sound field and acoustic modes using the constructed GF.
  • Demonstrates good agreement between the simulated GF and its analytic approximation.
  • Validates the numerical approach for acoustic modeling.

Conclusions:

  • The developed geometric ray-tracing method is effective for constructing the Green's function.
  • This approach shows promise for low-frequency acoustic modeling, an area not typically covered by geometric methods.