# Ray-tracing semiclassical low frequency acoustic modeling with local and extended reaction boundaries

## TL;DR

This paper validates the ray-tracing semiclassical (RTS) method for low frequency acoustic modeling with complex boundary conditions, demonstrating its effectiveness in realistic room acoustics scenarios involving frequency-dependent materials.

## Contribution

The study extends the RTS method to handle local and extended reaction boundaries, including porous layers, for more accurate low frequency acoustic modeling in realistic environments.

## Key findings

- RTS accurately reproduces Green's function for complex boundaries.
- RTS results closely match finite element method in pressure and decay curves.
- RTS effectively models low frequency sound fields with diverse boundary conditions.

## Abstract

The recently introduced acoustic ray-tracing semiclassical (RTS) method is validated for a set of practically relevant boundary conditions. RTS is a frequency domain geometrical method which directly reproduces the acoustic Green's function. As previously demonstrated for a rectangular room and weakly absorbing boundaries with a real and frequency-independent impedance, RTS is capable of modeling also the lowest modes of such a room, which makes it a useful method for low frequency sound field modeling in enclosures. In practice, rooms are furnished with diverse types of materials and acoustic elements, resulting in a frequency-dependent, phase-modifying absorption/reflection. In a realistic setting, we test the RTS method with two additional boundary conditions: a local reaction boundary simulating a resonating membrane absorber and an extended reaction boundary representing a porous layer backed by a rigid boundary described within the Delany-Bazley-Miki model, as well as a combination thereof. The RTS-modeled spatially dependent pressure response and octave band decay curves with the corresponding reverberation times are compared to those obtained by the finite element method.