End corrections at both ends of a flue instrument

We describe a study of end corrections for a soprano recorder sounding its lowest note (C5). Using both experiments and simulations, we have determined how the oscillation amplitude for the density standing wave in the interior of the instrument varies with position along the flue pipe. At the so-called open end, i.e., the end farthest from the mouthpiece, this amplitude extrapolates to zero (i.e., a node), a short distance beyond the physical end of the pipe, by a distance that agrees well with the theory of Levine and Schwinger [1] and subsequent work. This end correction is found to be independent of blowing pressure. At the blown end, i.e., the end of the instrument where an air jet emerges from the channel, the amplitude of the pressure standing wave is much larger than at the open end. For the lowest blowing pressures studied, for which the note is flat by about a semitone, this pressure amplitude is about 40% of the peak amplitude found near the center of the pipe. Some implications of this relatively large pressure amplitude at the blown end and how it varies with blowing pressure are discussed. H. Levine and J. Schwinger, Phys. Rev. 73 (4), 383–406 (1948). [Work supported by U.S. National Science Foundation (Grant No. PHY-2306035)]