Sympathetic Resonance?

[GreenWood]

I understand well enough how the sound wave forms in a flute, and around first open tonehole is the effective end of flute in 2nd octave also, where full venting is allowed below that.

[...]

You yourself say the wave is cut in half, so my reason tells me that you agree there are two waves. One inhabits the region towards the embouchure and the other towards the lower end.

I say this without malice, but what you write about sound waves (and acoustics) doesn't make any sense to me. If you're really into that sort of stuff, you might find it useful to get a better understanding of complex waveforms, standing waves and the acoustics of open tubes, instead of speculating about where this or that wave might "inhabit" in the bore of the flute. Here's a nice introduction to the acoustics of flutes

Oh, I think I take criticism for whatever it is worth. For example ad hominem is supposed a failure to argue rationally, or condescension might be seen as prejudiced conceit or even a form of assumed entitlement. Etc.

I don't expect my view to be understood, and frankly I'm really not into the mathematical representation of waveforms and similar, but take a more "mechanical" approach. I will explain the difference. Mathematical models are drawn from measurements of the resulting waveform from any particular arrangement. From those a picture is deduced of how the whole has interacted at any one point in time, and the parameters that effect that whole are calculated into a reliable equation. That is fine by me, it works, and I understand the picture it represents.

My view though is based on trying to understand the detail of how a waveform is achieved based on a progressive sequence of realtime events. That is to say, I am looking at how one particular pressure wave acts as it reflects at the end of the bore, interacts with similar on its return journey, and around TH1 has the effect of interfering with an incoming wave to the extent of shifting its pitch higher, so setting up a new standing wave pattern that suits bore length, not TH1 frequency. There is no other way I can think of for D2 (TH1 lifted) to sound but by interaction from a reflected wave at bore end, a flute will just play C# at TH1 otherwise.

Either way, the wave of D2 in lower part of flute will be different from higher part, they will not be mirror of each other because pressure differences at ends are different, bore characteristics are different along each part, TH1 is situated differently to ideal node position for each half. The result will be that the wave shape (sound not length) in lower bore, will be different and influence that of the top half by interference with it - in other words it creates a new sound based on the reflection of the wave formed in the lower bore. At this point we are talking soundform, not wavelength, because the wavelength has already become harmonized to D2.


I'm ok to agree to disagree, and do not mean to complicate how others approach all of this.

[paddler]

No matter how you look at it, there is no sympathetic resonance going on here. There is only one bore and only one air column.
Its just resonance! Nothing sympathetic about it. Pre-existing science explains all of this perfectly well, analytically, mathematically,
mechanically, and physically. You can even verify it practically, as many have already done.

It is not a new result or just someone else's speculation. There is real, peer-reviewed, science on the subject. It has all been thoroughly
documented for well over a century, and is covered in most text books on musical acoustics. People build real instruments and even
computer-based simulations of instruments, on this foundation.

It may sound old fashioned, but there are real advantages, both to yourself and the community as a whole, to taking the time to read
and understand what is already there in the literature. As Isaac Newton once said, "If I have seen further, it is by standing on the shoulders
of giants".

I have also heard people try to argue the corollary, "If I haven't seen further, it is because giants were standing on my shoulders". But maybe
here we can at least try not to stand on each other's feet!

[Flutern]

Greenwood, I'm not being condescending, I'm just pointing out that you have an incorrect understanding of sound waves. if you don't expect your view to be understood, how is this supposed to lead to a constructive discussion?

[Flutern]

It may sound old fashioned, but there are real advantages, both to yourself and the community as a whole, to taking the time to read
and understand what is already there in the literature. As Isaac Newton once said, "If I have seen further, it is by standing on the shoulders
of giants".

A nice variation on this theme: "we'll be a lot longer discovering the future if we don't recover the past" (John Mathieson Anderson)

[GreenWood]

Flutern, I didn't say you were. My reply was in the sense that you sort of implied I might take being suggested to badly, i.e. that in itself is just a tad demeaning. Clearly, people read the tone anything is written in so

"There's a ton of info at ... and that might explain something"

Is quite different from

"Why don't you go and learn some basics before confusing everyone"

But, funnily, I'm much easier with being told than talking around in circles, just because it is that obvious. I took your suggestion as well meaning, incidentally


Paddler, I'm fine with your definition, and have said so. Resonance is sympathetic, and as far as I know always. A molecule will move sympathetically to the behaviour of any neighbouring it.

For the mechanics and physics I don't think it is fully understood. Maybe I am not up to date with the latest, but there are details that are not explained as far as I know.

For example

https://www.physicsforums.com/threads/o ... ts.657511/

"As their introduction rightly says, "this involves the interaction between three different phenomena none of which are well understood"."

http://www.ece.uvic.ca/~bctill/papers/n ... n_1976.pdf

And sure, the paper is '76 , but the exchange is 2012 I think. There are various other details poorly defined, Benade describes several for example where he gives clear mathematical instruction but where detailed physical explanation is lacking, and understandably.


So for the example we were talking of, are you saying reflection from D1 sets edgetone and that stops C# from sounding, or would you say the waveform of D2 does not allow C# to sound for some reason, as in it shifts the pressure node somehow? I am able to play the two as a beat for a moment, where does that C# wave then go ??? If I close all toneholes below and the end of the bore the flute plays C# well, just as it does with all toneholes open. If I slowly uncover bore end it rises smoothly to D2. This seems to tell me that it is not resonance per se but impedance that is setting pitch. That is part of what I was saying re. Terry's piccolo.

Anyway, "peace bro" (and I guess you'd have seen these, but others not)




(Chlandi waves on a soap bubble in a flute, the pattern is from the film resonating and not a direct picture of pressure pattern across a flute, but I guess air might well also hold its own patterns somehow. From researchgate.net/publication/228923308_Visualization_of_sound_waves_using_regularly_spaced_soap_films )

[Flutern]

Flutern, I didn't say you were. My reply was in the sense that you sort of implied I might take being suggested to badly, i.e. that in itself is just a tad demeaning. Clearly, people read the tone anything is written in so

"There's a ton of info at ... and that might explain something"

Is quite different from

"Why don't you go and learn some basics before confusing everyone"

But, funnily, I'm much easier with being told than talking around in circles, just because it is that obvious. I took your suggestion as well meaning, incidentally

Fair enough, I could have worded that in a more diplomatic manner, so good on you for taking my comment for what it was intended to be. But let me quote you:

Paddler, I'm fine with your definition, and have said so. Resonance is sympathetic, and as far as I know always. A molecule will move sympathetically to the behaviour of any neighbouring it.

Now, that's what I find frustrating: you say that you are ok with Paddler's definition, and then you redefine sympathetic resonance in your own way Resonance is not always sympathetic, as Paddler explained, it happens when two bodies/systems interact: one produces a frequency, and another one starts resonating at that frequency, which is one of its resonant frequencies. Sympathetic resonance is not about molecules moving around: those are just the medium that carries the oscillation pattern.

Take a cello for instance: if you play a D on the low C string, the high open D string will start vibrating because its fundamental frequency matches the 2nd harmonic of the low D. The vibration of the open D string in that case is an example of sympathetic resonance, but the vibration of the low C string playing low D is not.

For a more geeky and unexpected illustration of sympathetic resonance, see how Janet Jackson had the power to crash computers

[GreenWood]

Resonance is about molecules moving about, because in physical matter the resonance is an expression of compression and expansion between those, whether in a string or in air. The momentum at work might be the weight of the string or it might be the velocity of a fluid, but the macro period of oscillation which is what you are observing is still caused by a sympathetic action between those molecules. In other words, at whatever scale, a resonance occurs as a repetitive cycle of distance between two points, be it guitar top moving up and down, two molecules moving towards and away from each other, and so on.

One molecule at the scale we are talking of will not resonate, it will just sit there. If you attach two together (i.e. a metal string) and pull them apart slightly and let go they will bounce towards and away from each other continuously, i.e. a resonance will be set up, and each molecule will be moving sympathetically with regards to the other.

This is the difficulty though, a physicist might take empirical measurements on a flute of say pressure and frequency, reduce a mathematical equation that works, and give a good macro interpretation of what is occuring. That is what we have I think.

Going on from there we are into fluid dynamics and quantum mechanics. These by nescessity are largely modelled, because we cannot study empirically in detail at that scale. The statistical modelling used can provide details , but it is not absolute or empirical.

For example, and I might have the calculation wrong but it is very rough either way, for fun I tried to figure what size screen would be needed to picture just one molecule wide sheet of air across the bore of a flute, where each molecule is a pixel, and it worked out at 1 km sq......and there is a flute length of those, and they are all doing what they do with all different sorts of pressure, vents, water droplets and so on flying around on a flute with many many other variables. I'm not sure if all the computers in the world working on what is occuring could find an acceptable model of one seconds playing within a year, and if they did it might not be applicable to the next second of playing.

So that is why I am quite happy just staying with observed effects, even if I cannot explain those. If I cannot find what happened to the C# note then I will have to imagine Schrodinger's cat ate it, or something along those lines. It doesn't really matter, because the flute works all the same.

This link has some interesting resources

https://fyfluiddynamics.com/2018/01/thi ... 1406250000

[paddler]

Greenwood, you seem to be trying to argue that sympathetic resonance and resonance are the same thing. They are not.

In musical acoustics and musical instrument design, sympathetic resonance is a widely used term that means something more than, and distinct from,
resonance. Sympathetic resonance is normally discussed in the context of stringed instruments, where an undamped string that has not been struck,
plucked, or bowed, begins to vibrate spontaneously in response to the vibrations of a separate string. This is not a phenomenon that is restricted to stringed
instruments, however. For example, a tuning fork at rest can begin to vibrate in response to the vibrations of a close-by tuning fork that has been struck.

To apply the concept of sympathetic resonance, meaningfully, to wind instruments, such as flutes, you would need to have two separate air chambers, with
the vibrations of one air chamber inducing vibrations in the other air chamber. But this is not the case in flute acoustics. There is only one air chamber, open
at both ends, and defined by the bore parameters, embouchure hole, foot opening and open tone hole lattice. Sound waves bounce back and forth within this
single chamber, and there is no other air chamber to resonate sympathetically with it. Hence, it is not sympathetic resonance. But see later in my post a
discussion of sympathetic vibration which is a different concept entirely, i.e., a different term with a different meaning in the context of musical acoustics.

The air chamber in a flute resonates at certain frequencies and not at other frequencies based on how the pressure nodes and antinodes of the potential
wave forms align with the open ends and open tone holes. When you close a tone hole you have the possibility of enabling resonance at a frequency that
was previously disabled because of the alignment of that previously open hole with a pressure antinode of a waveform at that frequency. The new resonant frequency
may be higher or lower than the old one.

Based on this common understanding of flute acoustics, there is nothing surprising about the example you gave. It is simply a matter of how the pressure nodes and
antinodes align with the open tone hole lattice. If you look back through my replies you will see that this is the point I have been making all along. Tunborough
even contributed the specifics of the node and antinode locations for your example, and others gave good examples of sympathetic resonance in the context
of musical instruments.

Now, it seems to me that you are confusing the terms sympathetic resonance and sympathetic vibration. Ordinary resonance is sometimes
referred to as sympathetic vibration, in a physics context. Your discussion of molecules etc is illustrating the role of sympathetic vibration in resonance
at a micro physical level, but this is really outside the context of musical acoustics, and does not seem to relate well to your original post and example.

But if your original post was using the term sympathetic resonance simply to mean sympathetic vibration (i.e., just resonance), then I think
we can agree that yes, there is resonance going on when your flute produces these notes. In fact, it is resonance that produces all the notes on all flutes.
But again, this is all very well understood and well documented in the context of musical acoustics, and is quite rudimentary in understanding how musical
instruments produce sound. So, I still recommend that you spend more time studying existing published material in this area. I think you might find it quite interesting
and enlightening.

[david_h]

What paddler is saying.

Except 'sympathetic vibration' is used so commonly (Wikipedia, Miriam Webster and many more) for sympathetic resonance that I think trying to use the two for different things can only cause confusion.

[GreenWood]

Well really my point was alluding to the choice of system you would call closed. Two molecules vibrating might be considered two closed systems in contact, just as you would use the idea of an entire air column as a closed system. It is relevant though, because the tendency is to confine the perception to only the parameter that suits, in this case an air column, when in fact there are various modes of observation of what is occuring. I will just scale it down a little, to give you one example.

"There is only one air chamber, open
at both ends, and defined by the bore parameters, embouchure hole, foot opening and open tone hole lattice. Sound waves bounce back and forth within this
single chamber, and there is no other air chamber to resonate sympathetically with it."

That is true, but it is also true that in my example there are at least three separate air chambers, four if you count the embouchure separately, five if you count space to cork, more if tonehole cavities are included.



1 gives the pressure [correction - displacement ] antinode length for C#
2 gives a wavelength for a reflection of the resulting sound in lower bore (slightly smaller than D frequency because D register would be north of C#)
3 is not noticed because the C# vent does not allow a fundamental wave to form, but in terms of system pressure and subtle reflection of waves of that length it exists, i.e. if you play low D at one end of flute and listen at the other, the sound will not all dissappear because of the antinode.
4 is the eventual wavelength parameter of D2, or if you prefer D that doubles down the bore.

You notice that D2 is NOT at optimum under the vent, and you notice that C# (obviously flattened due to less venting with lower vents closed) does not sound along with D2, even though there is no obvious reason for it not to (i.e. it can be made to sound independently).

david_h is right that the definitions are confusing, however it is possible the confusion only arises becauses there is a tendency to try to assume that whatever the definition is it must only apply to an own model of perception. I understand your definition Paddler, what I am saying is that a pressure wave emerging at C# will not only vent C# at end but that it will also reflect and resonate within length 2 at a separate frequency by reflection , as well as return out of phase with C# to the embouchure.

So the sympathetic resonance here is not one of same frequency as per your example, it is one that is more reliant on the energy of an incoming wave which then gets tailored to a frequency corresponding to length 2. That is why the definition I suggested is relevant. Though C# won't amplify that wave for it being out of phase, it will feed it continuously, until at some point somehow the whole system shifts to D2.

You are maybe saying it is D reflection forced into a D2 wave by venting at the antinode, sort of a static model of results, which I also said works and that I am ok with. I don't think that is the whole (and fully relevant) picture though, and what I just described above is only a small part of other ways of understanding the influences and physics at work.

However, I am not trying to superimpose one view over another or give an answer. I am asking a question. What I just described might not be fundamental to how D2 ends up playing instead of C# , but the fact remains that C# does not sound when in theory there is no obvious reason for it not to. This shift of antinode "higher" and outside of pressure point offered , seemingly merging frequencies in the process, is one of the most obvious and simple effects found on a flute, and so far I haven't found an acceptable or complete enough or authoritative explanation for it. A wave as a single piece of string that wants to find best fit works, but it isn't "real" or complete as explanation, and my question seems to show that.

The antinodes for C# exist, why isn't that note being played also ?


I will take saying to read more basics as just an opt out from saying you cannot explain it properly either.

[Tunborough]

there are at least three separate air chambers, four if you count the embouchure separately, five if you count space to cork, more if tonehole cavities are included.

They aren't separate chambers. The bore is wide open between the segments you are marking off. The resonant frequency is determined by the response of the system-as-a-whole. Looking at pieces of the system separately may give you clues to the overall response, but you can't be sure it's the whole story.

"'When I use a word,' Humpty Dumpty said in rather a scornful tone, 'it means just what I choose it to mean — neither more nor less.'"

[paddler]

but the fact remains that C# does not sound when in theory there is no obvious reason for it not to.

Your theory does not give you an obvious reason for it not to, because your theory is flawed!

The most fundamental flaw in your theory is that the reflection points you identify in the middle of your sequence of hypothetical air chambers do not actually exist.
Flute bores do not have separate parts that are each resonating at different frequencies. By starting with this assumption you lead yourself down a fruitless path, and
by sticking to this when others have already pointed out the error, simply wastes everyone's time.

Existing theory, which has been tried, tested and proven, does explain the phenomenon, as I, and others, have already explained in this thread. Specifically, the
C# waveform has a pressure antinode at the location of a tone hole that is closed when it sounds, and open when it does not sound. Pressure antinodes (points at which
pressure fluctuates maximally), can not occur in locations that have leaks that connect the bore's air chamber to the outside air. Pressure nodes, which are displacement
antinodes (i.e., places where air movement is maximized) can occur at these locations. This is what happens at the embouchure, for example, where air moves rapidly
in and out of the bore at the frequency at which it is resonating. The player's breath is the only source of energy that keeps this resonance from dying out (which would
naturally occur due to frictional energy loses if there where no supply of energy).

Your inability to understand such explanations highlights your lack of understanding of the meaning of the basic concepts that underly existing theory. Your further misuse of
those terms in the examples you post just betrays this misunderstanding further. Fortunately, there are a lot of resources available on line, and in books, to help one
understand existing theory on musical acoustics. I think your best solution is to study it, and then come back to the explanations that have been posted in this thread
to see if you can understand them yet, or at least highlight the specific areas of misunderstanding so that people can help you. By framing your questions in the context of
existing terminology and well-studied and accepted theory, you stand a better chance of homing in on the source of your misunderstanding than you do by continually trying
to push your own personal, flawed, theory and forcing the discussion back into that context.

[GreenWood]

I corrected the pressure/displacement antinode you mention, that was a "typo" or similar.

"The most fundamental flaw in your theory is that the reflection points you identify in the middle of your sequence of hypothetical air chambers do not actually exist."

All the examples of standing waves I find give the open end as reflection point of an initial pressure/sound wave, and they all say that this length sets the resonant frequency because of that . That would make between embouchure and an open C# tonehole a chamber length, because this is where the wave reflects (end effects being not relevant for now). So why you are telling me to read up on theory that you then say is flawed defies me.

Beyond that you have a pipe with two open ends, I call that a chamber. How can you say it is not also a (separate) chamber ?

Sound from end of first chamber travels through the second, and though not as a standing wave, it will cause some form of resonance to occur there.

It is obvious that the second chamber eventually integrates with the first, when D2 sounds.

The point just seems very obvious, and I could not explain it more simply I think.

Oh well.

[Tunborough]

http://newt.phys.unsw.edu.au/music/flut ... roque.html

[Flutern]

There's none so deaf as those who will not hear...