Sound production in recorderlike instruments. I. Dimensionless amplitude of the internal acoustic field

Abstract

Data on the internal acoustic pressure signals in an experimental recorderlike flue organ pipe are presented. A dimensionless representation appears to be a powerful basis for the analysis of these data. The dimensionless amplitude of the fundamental is, for a given geometry, a function of the Strouhal number only. For the first hydrodynamic mode of the jet, this amplitude is independent of the acoustic mode involved. The dimensionless amplitude of the second harmonic displays two different behaviors, depending on whether the jet is laminar or turbulent. This specific Strouhal number dependency implies a strong influence of the distance W from the flue exit to the labium on the timbre of recorderlike instruments. In recorders the ratio W/h, where h is the height of the flue exit, is adjusted by craftsmen to a value close to 4. This specific ratio ensures an optimal harmonic content to noise ratio in the produced sound. Increasing the distance W yields a more powerful sound but at the expense of additional turbulence noise. For these large ratios W/h, transitions between different hydrodynamic modes of the jet are observed at low blowing pressures. This phenomenon is avoided by the choice of a recorderlike geometry.