Sympathetic Resonance?

[Flutern]

Greenwood, try to pronounce the sound 'sh': when you do that you have two loosely coupled chambers in your mouth: one at the back of where the blade of your tongue approaches the palate and one at the front. In that case the acoustics of the two cavities ( or chambers) are pretty much independant for all practical purposes. But that's no longer the case as soon as you make that constriction wider, as in English 'r' for instance.

You would need a drastic constriction in the bore of the flute to have two chambers. The chambers you imagine at the tone holes or at the stopper are simply the result of your lack of understanding of acoustics.

Errare humanum est, perseverare diabolicum

[paddler]

"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.

Greenwood, I think one of the points you are still failing to grasp is that the open tone holes do not serve to end the bore and create a reflection point.
If they did, then closing tone holes below some open hole would have no effect. Clearly in your examples, opening and closing tone holes downstream
of some number of open tone holes IS having an effect, in that it is changing the pitch. This is the behavior that you tell us you are struggling to explain.
But it is explained, quite simply, when you accept that those open tone holes do not terminate the bore for the frequency ranges you are considering.
In fact, the precise details of this explanation have already been presented to you numerous times in this very thread.

The second problem with your flawed explanation is that only the first of your hypothetical air chambers actually has an energy source to drive its resonance.
That is the one that has the embouchure. Your notion that some separate air chamber, lower down the flute bore, can resonate based on the vibrations of the
hypothetical chamber above it, and at a different frequency, is also flawed, for the following reason.

If two adjacent air chambers were resonating at different (unrelated) frequencies, and connected by what you consider to be a reflection point in mid air,
the mismatch in the timing between the fluctuations in pressure at that point would prevent any resonance. Quite simply, you need to have synchronization
in the timing of the energy pulses in order to have resonance. Without that synchronization, there is no energy source to sustain the resonance of your
hypothetical second chamber.

On the other hand, if the two chambers do phase lock such that the pressure pulses are occuring at precisely the same time, and reinforce each other
to sustain resonance, then what you have is a single large chamber that is resonating at a single frequency, not two separate air chambers. The thing that
you are referring to as a reflection point is actually a pressure antinode within that single chamber. Opening a tone hole at that point does not terminate the
bore and create a reflection point, as you hypothesize, since the portion of the bore downstream of it will still be resonating! Opening the tone hole simply creates
a leak (and a large one!) right at the point where the current resonance requires pressure to fluctuate, with little to no energy loss, at the frequency of resonance.
By introducing a leak here, you cause a loss of energy that prevents the air chamber from resonating at that frequency, but it does not necessarily prevent it from
resonating at other frequencies that do not have pressure antinodes at that location. This is the standard theory, and it explains the behavior you are observing
quite simply and elegantly.

Your theory, which is flawed in numerous ways, as I have pointed out, does not explain the behavior you are observing, as you yourself have pointed out!
The responsible thing to do, when one's theory does not agree with the behavior observed in practice, is to accept that the theory is flawed and to try to
come up with a better one. In this case you are lucky, in that a better one already exists, and is both proven and well documented. Our advice to you has
simply been to take the time to understand it, rather than keep flogging a flawed theory of your own.

Perhaps another more basic point you are missing is that when second and third octave notes are played, they have the air chamber resonating at high
frequencies, and the wave length of these high-frequency sound waves is such that the wave form repeats itself within the bore. In other words, at these
high frequencies there are several pressure nodes (displacement antinodes) and several pressure antinodes (displacement nodes) within the single resonating
air chamber of the flute's bore. A leak at any of these pressure antinodes for a particular frequency will generally be enough to prevent the bore from resonating
at that frequency.

OK, so I think I have done more than enough due diligence in trying to point you in the right direction, even to the point of trying to explain things in terms
of your confusing and ultimately invalid theories of flute acoustics. That was purely for your benefit, because it is a bit of a waste of time for the rest of us.
Now maybe you can do us all a favor and simply take the time to get up to speed with what is already out there.

[paddler]

"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 ?

One last thing that I intended to cover in the last post.

Take a closer look at what happens at the open ends of a resonating air chamber, for example at the embouchure and foot of a flute. At these reflection points you have
constant pressure equal to external pressure. The pressure at these points does not change, so these are pressure nodes, and hence, displacement antinodes, i.e., points
where air movement is maximized.

Now contrast this to what is happening at a pressure antinode point within the bore, i.e., a point where pressure changes are maximum, but at which there is no air movement.
I hope you can see that what is happening at these points is the opposite of what is happening at reflection points. So you can't reasonably claim that these are equivalent to
each other when they are in fact opposite behaviors.

[david_h]

The use of the word 'reflect' for both what happens to a sound wave at the end of an open pipe and what happens when a sound wave reaches the wall of a room can be confusing. At both energy comes back in the opposite direction but In terms of molecular displacement they may not be the same.

[Tunborough]

The use of the word 'reflect' for both what happens to a sound wave at the end of an open pipe and what happens when a sound wave reaches the wall of a room can be confusing. At both energy comes back in the opposite direction but In terms of molecular displacement they may not be the same.

Ah, David, I'm glad you brought this up. Both cases are total reflection (or at least nearly so). But - and here you've hit on the magical part - there's a difference ...

Consider a high-pressure pulse that travels down a tube and hits a closed end, like a uilleann chanter on the knee. The high pressure pulse will bounce off the closed end, and be reflected back as a high-pressure pulse in the opposite direction. But when a high-pressure pulse hits an open end, the air in the pulse rushes out to freedom and, with inertia, it pulls out even more air to follow it. This leaves an area of low pressure, which starts moving back up the tube. The high-pressure pulse has been reflected from the open end as a low-pressure pulse.

Almost 50 years ago, my high-school physics teacher had a device that could demonstrate this positive reflection and negative reflection. It was amazing. I wish there were more opportunities to see it happening in the real world.

When a high-pressure pulse hits an open tonehole as in OXX XXX, it gets partially reflected: a smaller low-pressure pulse is reflected back, and a smaller high-pressure pulse continues on down the tube.

[skap]

Maybe Greenwood's problem is that he is thinking about individual
sound pulses propagating in the bore rather than standing waves.
(Is that what he calls "more mechanical point of view")
Any such argumentation may only apply to the transitional stage
when the standing wave is not yet settled.

If you think of an individual pressure pulse propagating down a
flute's bore, it SHOULD partially reflect back from a vented hole,
as there's an abrupt decrease of impedance there, but the other part
will continue forward, reflect from subsequent vented holes, and
eventually from the open end. So, at least at some very early stage,
one can imagine a picture of reflected pulses going forth and back
within their "chambers" at frequencies defined by the lengths of these
"chambers", as well as penetrating the neighboring "chambers". That's
a speculation, but seen like that, it is not necessarily as
anti-scientific as I first thought it was.

By the way, I think, Eric Heller's book is much better at explaining things
than most other books on acoustics I've opened. In the Chapter 1 (available
as a sample), you have the acoustic impedance, and the reflections
from open/closed tube end, very clearly explained.

https://www.whyyouhearwhatyouhear.com/s ... ample.html

[paddler]

Consider a high-pressure pulse that travels down a tube and hits a closed end, like a uilleann chanter on the knee. The high pressure pulse will bounce off the closed end, and be reflected back as a high-pressure pulse in the opposite direction. But when a high-pressure pulse hits an open end, the air in the pulse rushes out to freedom and, with inertia, it pulls out even more air to follow it. This leaves an area of low pressure, which starts moving back up the tube. The high-pressure pulse has been reflected from the open end as a low-pressure pulse.

Exactly! Thank you Tunborough, that was a brilliant explanation! This is why the open ends of the chamber are displacement antinodes not pressure antinodes (i.e., pressure nodes not displacement nodes).

The degree to which open tone holes behave like the open end of a flute depends on their size and, critically, the frequency of the sound wave.
For low frequency sound waves an open tone hole may be large enough to cause reflection, just as the end of the flute would. This is what it means
to say that an open tone hole terminates the bore. For most flutes, this is the behavior we have in the lowest octave, and I think this is the
behavior that Greenwood is assuming occurs at all frequencies.

However, at higher frequencies, typical of second and third octave notes on our flutes, and for tone hole sizes typical of our wooden flutes, the tone
holes are not large enough to terminate the bore. This is why cross fingering is effective. It is also why baroque and renaissance flutes (both of which have
relatively small tone holes) make such extensive use of it. Finally, it is why behaviors such as the ones discussed in this thread occur in higher octave notes
on the flutes and whistles we use, but not necessarily in the lowest octave.

Take a look at this brief paper which discusses precisely this point:

http://www.phys.unsw.edu.au/~jw/ICASmith&Wolfe.pdf

[david_h]

Yes, thank you Tunborough. Seems I was wise to leave the explanations to someone else.

Actually it was because it was too far in the past but I am finding that the book chapter recommended by skap covers it, and also impedance, in very intuitive way. Very readable. Thanks

[tstermitz]

Thanks Paddler. This gets at the questions I had in the original post.

In particular, I was wondering why C# OOO XXX had a nicer tone than OOO OOO. And yes, I've had to play around with different RH fingers and venting to make 3rd register notes either come into the correct pitch or to have a better resonance.

However, at higher frequencies, typical of second and third octave notes on our flutes, and for tone hole sizes typical of our wooden flutes, the tone holes are not large enough to terminate the bore. This is why cross fingering is effective. It is also why baroque and renaissance flutes (both of which have relatively small tone holes) make such extensive use of it. Finally, it is why behaviors such as the ones discussed in this thread occur in higher octave notes on the flutes and whistles we use, but not necessarily in the lowest octave.

[paddler]

Actually it was because it was too far in the past but I am finding that the book chapter recommended by skap covers it, and also impedance, in very intuitive way. Very readable. Thanks

I agree! I just finished reading through that chapter that skap posted a link to. It is excellent. Probably the best, and most readable, explanation I have seen, in fact.
The book itself is quite expensive new, but there are quite a few copies available on eBay for a fraction of the new price. I think this one would be worth owning,
for those who are interested in this kind of thing. In fact, I just grabbed one of the inexpensive, lightly-used, eBay copies to add to my library, so thank you for suggesting
that skap!

[paddler]

Let me just try to pull some of this back to specific questions Greenwood raised in the example that focused on various behaviors
of xxx xxx / oxx xxx / and ooo ooo fingering in first and second octave. I'm doing this in the hope of bringing some closure to
this, but please jump in if I've misrepresented something here.

Q1. Why does xxx xxx fingering give us first octave D?

A1. Because the wavelength of the sound wave at the frequency that corresponds to first octave D matches the length of the flute's
bore, plus compensating end corrections for the embouchure and foot opening. A single wave at the frequency of first octave D fits
the bore length.

Q2. Why does xxx xxx fingering also give us second octave D?

A2. Because that same bore length plus end corrections also fits two second octave D wave lengths, which are half the length of
first octave D waves. Rising an octave doubles the frequency and halves the wavelength. The same air chamber can resonate at
either frequency, and in fact resonates at both and at higher frequency harmonics in the harmonic series. The combination of all
of these harmonics, and the relative energy in each, determines the timbre of the notes.

Q3. Why does oxx xxx NOT give us first octave D?

A3. Because opening the top tone hole prevents the formation of the pressure antinode that is located half way between the pressure
nodes at the two ends of the flute. Hence, the bore can no longer accommodate that single wave length of low octave D.

Q4. Why does oxx xxx give us second octave D rather than C#?

A4. Because the resonating air chamber includes the lower portion of the bore at that higher frequency, and the length of this
sound chamber (physical length of bore plus end corrections for embouchure and foot) is divisible by the wavelength of the sound
wave for the frequency of second octave D. Second octave D can resonate when first octave D can not, because second octave
D does not require a pressure antinode at the location of the now open first tone hole. So this gives second octave D the same way
that xxx xxx does, but it explicitly prevents the formation of first octave D which is also a possibility for xxx xxx fingering. In order
to sound first octave C# with this fingering the bore would need to be longer.

Q5. Why does oxx xxx not give us C# in the second octave, or at least a note lower than C#, when ooo ooo does give us C# in the first
octave? Or stated another way, why doesn't the first open hole effectively define the end of the bore in both cases.

A5. Because for higher frequencies, the first open tone hole is not sufficiently large to terminate the bore. Hence, for these frequencies
the resonating sound chamber extends further down the bore, and the length of this chamber is such that two high frequency D wavelengths
will fit, but two high frequency C# wavelengths will not (they are longer!). Note that it is not even large enough to terminate the bore
for first octave notes, since oxx ooo will give C natural not c#.