dorsal/arxiv
View SchemaOptimized interpolations and nonlinearity in numerical studies of woodwind instruments
| Authors | A. Skouroupathis, H. Panagopoulos |
|---|---|
| Categories | |
| ArXiv ID | physics/0509055 |
| URL | https://arxiv.org/abs/physics/0509055 |
| DOI | 10.1121/1.4787634 |
| Journal | Acta Acustica united with Acustica, Vol. 91 (2005), supp/1 |
Abstract
We study the impedance spectra of woodwind instruments with arbitrary axisymmetric geometry. We perform piecewise interpolations of the instruments' profile, using interpolating functions amenable to analytic solutions of the Webster equation. Our algorithm optimizes on the choice of such functions, while ensuring compatibility of wavefronts at the joining points. Employing a standard mathematical model of a single-reed mouthpiece as well as the time-domain reflection function, which we derive from our impedance results, we solve the Schumacher equation for the pressure evolution in time. We make analytic checks that, despite the nonlinearity in the reed model and in the evolution equation, solutions are unique and singularity-free.
{
"annotation_id": "d5e5f699-a138-48bf-87c9-75a9e37b5204",
"date_created": "2026-03-02T18:01:00.819000Z",
"date_modified": "2026-03-02T18:01:00.819000Z",
"file_hash": "dfd6cc58657f66c15ad7b8504959cc900364a492a4aaaae014f3a39ece9c1d41",
"private": false,
"record": {
"abstract": "We study the impedance spectra of woodwind instruments with arbitrary\naxisymmetric geometry. We perform piecewise interpolations of the instruments\u0027\nprofile, using interpolating functions amenable to analytic solutions of the\nWebster equation. Our algorithm optimizes on the choice of such functions,\nwhile ensuring compatibility of wavefronts at the joining points. Employing a\nstandard mathematical model of a single-reed mouthpiece as well as the\ntime-domain reflection function, which we derive from our impedance results, we\nsolve the Schumacher equation for the pressure evolution in time. We make\nanalytic checks that, despite the nonlinearity in the reed model and in the\nevolution equation, solutions are unique and singularity-free.",
"arxiv_id": "physics/0509055",
"authors": [
"A. Skouroupathis",
"H. Panagopoulos"
],
"categories": [
"physics.comp-ph",
"physics.gen-ph"
],
"doi": "10.1121/1.4787634",
"journal_ref": "Acta Acustica united with Acustica, Vol. 91 (2005), supp/1",
"title": "Optimized interpolations and nonlinearity in numerical studies of woodwind instruments",
"url": "https://arxiv.org/abs/physics/0509055"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "8f45454d-6125-4e14-8895-69bf271f3c7a",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}