Measured Spectrum of Stopped Wood Organ Pipe Shows ALL Overtones

[greypilgrim]

TL;DR

Why are the even-numbered overtones not suppressed?

Hi.

I have a wooden organ pipe with removable stopper and wanted to confirm the theoretically predicted spectra using a smartphone app. The formulae for the fundamental frequencies for the open and stopped cases work quite well, with the stopped pipe being about an octave lower.

However, theory also predicts that the even-multiple overtones should be absent in the stopped case (or at least clearly weaker than the odd ones). The spectrum does not exhibit this at all, I can clearly see all multiples of the fundamental with no clear pattern for the amplitudes. Same with a clarinet (which should behave like a stopped pipe as well); and I also used different apps and an iPad at some point.

Of course real instruments do not behave ideally, but I observed no indication of suppression of even-multiple overtones at all. Why?

 

[Andrew Mason]

TL;DR: Why are the even-numbered overtones not suppressed?

I have a wooden organ pipe with removable stopper and wanted to confirm the theoretically predicted spectra using a smartphone app. The formulae for the fundamental frequencies for the open and stopped cases work quite well, with the stopped pipe being about an octave lower.

However, theory also predicts that the even-multiple overtones should be absent in the stopped case (or at least clearly weaker than the odd ones). The spectrum does not exhibit this at all, I can clearly see all multiples of the fundamental with no clear pattern for the amplitudes. Same with a clarinet (which should behave like a stopped pipe as well); and I also used different apps and an iPad at some point.

Of course real instruments do not behave ideally, but I observed no indication of suppression of even-multiple overtones at all. Why?

Seems that you may have a leaky pipe stopper. If the stopper is not tight to the wood you will get even and odd harmonics because the pipe is acting as both a closed and open pipe.

AM

 

[Orthoceras]

TL;DR: Why are the even-numbered overtones not suppressed?

However, theory also predicts that the even-multiple overtones should be absent in the stopped case (or at least clearly weaker than the odd ones). The spectrum does not exhibit this at all, I can clearly see all multiples of the fundamental with no clear pattern for the amplitudes.

In support of your point, see below two spectra I recorded just now from a wooden organ pipe in two situations. In the closed pipe the third harmonic is suppressed, while the second harmonic is present. The stopper is not leaky. Apparently the spectrum of a fairly wide, real pipe is more complicated than the ideal one.

 

[Baluncore]

In the closed pipe the third harmonic is suppressed, while the second harmonic is present.

It would appear that the stop is positioned such that it cancels the 2kHz tone rather well.

 

[Andrew Mason]

In support of your point, see below two spectra I recorded just now from a wooden organ pipe in two situations. In the closed pipe the third harmonic is suppressed, while the second harmonic is present. The stopper is not leaky. Apparently the spectrum of a fairly wide, real pipe is more complicated than the ideal one.


View attachment 369682

A closed pipe with a fundamental frequency of 667 Hz should have overtones of 2001, 3335, 4669 Hz etc corresponding to odd multiples of the fundamental. The open pipe at fundamental 667 Hz should have overtones of 1334, 2001, 2668, 3335, 4002, 4669 Hz.

In a wooden pipe, the vibrations in the wood may suppress or enhance overtones. The wooden organ stops are designed (voiced) to absorb some overtones to produce a softer sound. This may be the reason the 2001 Hz overtone is suppressed.

However, resonance of the stopped pipe for the second and fourth overtones means that an antinode is present at the stop position. That means the sound waves for these overtones is not affected by the stopper’s presence. How have you determined that there are no leaks in the stopper?

AM

 

[Orthoceras]

However, resonance of the stopped pipe for the second and fourth overtones means that an antinode is present at the stop position. That means the sound waves for these overtones is not affected by the stopper’s presence. How have you determined that there are no leaks in the stopper?

(Shouldn't that be the second and fourth harmonics, instead of second and fourth overtones?)

When sliding the stopper through the organ pipe, it felt like a snug fit. In addition I tested for leaks in the stopper by blowing through the foot hole, while blocking the labium. No significant amount of air escaped.