Physical modelling of a spring reverb tank incorporating helix angle, damping, and magnetic bead coupling

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Abstract

Reproducing the main features of a spring reverb tank impulse response across the hearing range with a physical model presents unique challenges because of the high levels of coupling between the spring’s vibrational polarisations. Previous attempts based on a model that includes helix angle can accurately simulate helical spring vibrations, but see discrepancies in reproducing measured impulse responses due to heavy simplifications in specifying boundary conditions and input/output mechanisms. This paper presents an improved physical modelling approach by incorporating magnetic bead dynamics and frequency-dependent damping. The beads are modelled as coupled beams using a thin form of the spring equations that reduces to thin beam equations in the absence of curvature. Also ensuring the correct geometric alignment between the beads and the spring, the model’s response to rotationally driving the input bead is shown to display the expected mixture of waves travelling along the different spring polarisations. To achieve a similar damping profile as observed in measured impulse responses, different damping parameters are set for each polarisation, leading to non-proportional damping and multiple decay rates within small frequency bands. The new formulation results in the main features of measured impulse responses now being reproduced well.
Original languageEnglish
Pages (from-to)312–330
Number of pages19
JournalJournal of the Audio Engineering Society
Volume73
Issue number6
DOIs
Publication statusPublished - 04 Jun 2025

Keywords

  • physical modelling
  • spring reverb tank
  • magnetic bead coupling

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