Theory of Flue-Pipe Sound Generation
Samuel A. Elder · The Journal of the Acoustical Society of America · 1965
External radiated sound in the near field of the mouth of flue organ pipes or recorders is in phase with the internal field and may be calculated from the standing-wave-pressure amplitude within the pipe (Nyborg's law). Pipes voiced for small-mouth radiation impedance are driven at (approximately) a velocity antinode. Here the jet-edge system possesses asymmetry under dynamic conditions. The external sound-pressure amplitude, being proportional to the standing-wave flux in the mouth, depends only on jet speed and cross section, independent of pipe Q, since the standing-wave flux is comparable to jet flux. When voiced for larger-mouth impedance, the driving point approaches a velocity node condition. As this happens, the jet-edge system becomes symmetrical. Most efficient driving occurs when the peak sound pressure near orifice approaches jet stagnation pressure, since this case represents best “matching” to driver. With recorders, best match occurs for notes near the middle of the scale, causing the instrument to be loudest in this range. [Work supported by the U. S. Office of Naval Research.]