Speaker
Description
Sound propagation in brass instruments is dominated by spatial and non-linear effects arising from high sound pressure levels. To simplify analysis, one-dimensional linear frequency-domain models, such as the Transfer-Matrix Method, are commonly used to calculate the input impedance of brass instruments. These models neglect non-linear effects and typically assume planar or spherical wave propagation. Finite Element Methods in the frequency domain can improve accuracy for linear spatial wave propagation, particularly for sound radiation from the instrument’s bell. While effective for low-volume, linear regimes, these methods are limited in capturing non-linear dynamics.
To address wave propagation across the full volume range, time-domain models offer a more suitable approach as they account for non-linear effects like wave steepening. In engineering, the one-dimensional Method of Characteristics (MOC) is a proven tool for simulating pulsations in piping systems, known for its low diffusion and dispersion errors compared to other numerical methods.
This study extends the MOC to spatial problems through a dimensional splitting method, enabling the modelling of non-linear behaviour within brass instruments and non-planar wave propagation in their bells. Non-reflective boundary conditions are implemented to accurately simulate sound radiation into the far field. Results are evaluated and compared with those from linear models, demonstrating the advantages of the extended MOC for capturing complex acoustic phenomena in brass instruments.
