Measuring the behavior of the acoustic standing wave exiting a flue organ pipe: Is the decay sinusoidal or exponential?

Abstract

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.