Foot resonance in an organ pipe

Pressure measurements in the foot of an organ pipe under playing conditions show acoustical pressure fluctuations induced by the acoustic field in the pipe. Fluctuations of the pressure difference between the foot and the mouth of the instrument results in jet velocity fluctuations that can absorb or produce acoustic energy depending on relative phase with the acoustic pressure in the mouth of the pipe. In most flue organ stops, pipe dimensions indicate that the first pipe resonance and the Helmholtz foot resonance should lie close to each other at least for one pipe in the stop. The present work was triggered by the question of knowing why this does not seem to bother organ builders. Measurements of Helmholtz foot resonances as a function of the driving pressure carried on a pipe with adjustable foot volume are presented. Measurements indicate a damping of the resonance due to the flow through the mouth that can be accounted for by an elementary model of the flow through the mouth. Analysis indicates that, unlike recorder playing, the jet velocity guarantees an efficient damping.