Inhomogeneous diffusion process in elongated rooms: An interpretation based on the dynamics of sound particles

Area of Science:

• Acoustics
• Physics
• Room Acoustics

Background:

• Reverberant sound fields in elongated rooms exhibit non-homogeneous diffusion.
• Understanding this phenomenon requires a deeper physical interpretation beyond standard diffusion models.

Purpose of the Study:

• To physically interpret non-homogeneous sound diffusion by analyzing sound particle dynamics.
• To propose and compute a local mean free path for sound particles.
• To estimate the spatial distribution of the diffusion coefficient.

Main Methods:

• Building upon original diffusion theory.
• Defining and calculating a local mean free path from particle paths.
• Estimating the diffusion coefficient's spatial distribution based on the mean free path.

Main Results:

• A novel quantity interpreted as a local mean free path was successfully computed.
• The estimated spatial distribution of the diffusion coefficient showed good agreement with direct estimations.
• The proportionality between mean free path and diffusion coefficient was utilized.

Conclusions:

• The particle dynamics approach provides a valid physical interpretation of non-homogeneous sound diffusion.
• The proposed local mean free path is a useful metric for characterizing diffusion in complex acoustic spaces.
• This method offers an alternative to direct Fick's law estimations for diffusion coefficients.