Revisiting the Open-End Reflection Coefficient and Turbulent Losses in an Organ Pipe with Low Mach Number Flow

The reflection coefficient of the open end belongs among the essential parameters in the physical description of a flue organ pipe. It leads directly to practical topics such as the pipe scaling. In this article, sound propagation is investigated inside an organ pipe with the most intense mean flow that is achievable under musically relevant conditions. A theoretical model is tested against the experimental data to obtain a suitable formula for the reflection coefficient when a non-negligible flow through the open end is considered. The velocity profile is examined by means of particle image velocimetry. A fully developed turbulent profile is found and interactions of the acoustic boundary layer with the turbulent internal flow are discussed. A higher value of the end correction than expected from the classical result of Levine and Schwinger is found, but this feature shall be associated with the pipe wall thickness rather than the mean flow effects.