Speaker
Description
A tube ending in an infinite baffle is a classical radiation problem and has been studied extensively, with closed-form or semi-analytical results for radiation impedance, directivity, and end correction. In contrast, an unflanged tube introduces additional physics, such as edge diffraction, making analytical treatment more challenging. This problem is highly relevant for simulating musical instruments based on resonances in tubes.Here, secondary sources are used to couple the interior and exterior domains of a partially open shoebox. Green’s functions between all secondary-source pairs are needed for both domains under rigid-walled boundary conditions. For the interior, a modal solution is used, while the exterior domain is modeled with an edge-diffraction integral-equation formulation.A rectangular tube with one open end and inner dimensions 10 cm × 10 cm × 60 cm was investigated. Measurements were made in an anechoic chamber, with a microphone placed near the bottom corner inside the tube and a tweeter loudspeaker positioned 2 m from the opening. The ratio of microphone pressure amplitudes was measured with the box present and in an otherwise identical free-field setup. The same scenario was simulated in MATLAB using a modal sum for the inside domain and an edge-diffraction-based toolbox for the outside domain.Measurements and simulations agree for the first six resonance frequencies, with a maximum deviation of 3.5 %. For these modes, the largest Q-factor discrepancy occurs for the first resonance and decreases for higher modes, likely due to physical losses not fully captured in the simulation.