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Correctly predicting the playing frequencies of a musical instrument is dependent on the length of the resonator with the addition of an end correction. There are multiple theories describing this end correction, perhaps the simplest being that the end correction of a pipe is a physical extension of the sinusoidal pressure standing wave inside the pipe. However, recent optical imaging of the flow in a flue organ pipe found an unexpected exponential decay of pressure just outside of the pipe. This work looks to validate those findings acoustically. A flue organ pipe was played at the 1st, 5th, and 7th harmonics and the pressure just inside and immediately outside the end of the pipe played was measured using a zero-degree PU Match Microflown sound intensity probe. These measurements were fit to both exponential and sinusoidal curves and compared to the optical images. While an exponential trend is in fact apparent in some cases, the goodness-of-fit appears to be dependent on which harmonic is sounding. Future work includes exploration of a potential transitional region, assessing the impact of altered pipe geometry (both cross-sectional shape and size), and investigating potential sensor interference by using other measurement equipment.
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This content will become publicly available on November 25, 2026
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/rdecay 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 beyondδfollows a robust 1/rdecay independent of model choice.
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- Award ID(s):
- 2109932
- PAR ID:
- 10655168
- Publisher / Repository:
- Acta Acustica
- Date Published:
- Journal Name:
- Acta Acustica
- Volume:
- 9
- ISSN:
- 2681-4617
- Page Range / eLocation ID:
- 71
- Subject(s) / Keyword(s):
- End correction, Flue organ pipe, Waveguide acoustics, musical acoustics
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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