Synchronization of organ pipes

TL;DR

This paper models the complex synchronization phenomena in coupled organ pipes using delay-coupled Van-der-Pol oscillators, providing analytical insights and experimental validation of the dynamics involved.

Contribution

It introduces a novel modeling approach for organ pipe synchronization using delay-coupled Van-der-Pol oscillators and analyzes bifurcation scenarios at Arnold tongue boundaries.

Findings

Model accurately predicts synchronization frequencies.

Bifurcation analysis matches experimental observations.

Delay effects critically influence sound weakening phenomena.

Abstract

We investigate synchronization of coupled organ pipes. Synchronization and reflection in the organ lead to undesired weakening of the sound in special cases. Recent experiments have shown that sound interaction is highly complex and nonlinear, however, we show that two delay-coupled Van-der-Pol oscillators appear to be a good model for the occurring dynamical phenomena. Here the coupling is realized as distance-dependent, or time-delayed, equivalently. Analytically, we investigate the synchronization frequency and bifurcation scenarios which occur at the boundaries of the Arnold tongues. We successfully compare our results to experimental data.