Comparing classical and empirical end correction models using spatial pressure measurements in flue pipes

This study evaluates end-correction behavior in flue organ pipes by comparing two models: the classical low-frequency expression of Levine and Schwinger and the empirical, frequency-dependent refinement of Davies et al. [Journal of Sound Vibration 72 (1980) 543–546], later revisited by Moore et al. [JASA Express Letters 3 (2023) 055002]. Using a Microflown probe, we performed high-resolution pressure measurements inside and outside circular and square pipes to capture the transition from standing-wave to radiating behavior. Sinusoidal variation within the end-correction region and 1/r decay beyond were observed, consistent with theory. A two-region curve-fitting approach quantified each model’s accuracy. In the tested range (0.049 ≤ ka ≤ 0.377), both models reproduced the data with nearly identical accuracy (R2 ≥ 0.997), with only a slight advantage for the classical form in one square-pipe case. Probe interference was evaluated and found negligible. While the analysis employs fixed end-correction values rather than a universal fit, it provides a controlled test of how well existing models capture the spatial pressure field near the pipe termination. Results indicate that both models are adequate in this regime, and that the radiating field beyond δ follows a robust 1/r decay independent of model choice.