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Discussion Starter · #81 ·
I'm not sure what you mean in questioning how much vibration effect the reed movement could have on the standing wave.
The standing wave is vibrating air molecules, and the air molecules are vibrated by the reed movement.

As I was trying to say; (I believe) the mouthpiece creates and gives character to the standing wave by resisting and reflecting the vibration of the reed.
Any vibration of the mouthpiece would be the result of its failure to completely resist and/ or reflect the reeds vibration.
Less resistance to, and less efficient reflection of reed vibration on the part of the mouthpiece should mean more absorption and dampening of the reed vibration. Like a passive EQ, the sound may be shaped by attenuating certain frequencies; or like a compressor, the sound may be shaped by the cutting off or limiting a part of the attack of each note.
One theory is that any resulting vibration of the mouthpiece produces a sound that is loud enough to be detected.
Another theory is that vibration of the mouthpiece tip (like a second, or double reed) mechanically effects or works in conjunction with the vibration of the reed, and alters the character of the vibrational sound production.
My belief is that the vibrating mouthpiece does not produce an audible sound, but (if vibrating), absorbs and/ or fails to reflect some part of the reed vibration as it is setting the air molecules into motion, and as the vibration of the molecules reflects off the baffle.

It is probably important to separate in our minds, the purely mechanical vibration of the reed (like as you note the reed hitting the tip, which is initially mechanical), from the air molecule vibration which we sense as sound.
Reed vibration would produce no actual sound in the absence of air (as in the vacuum of space), but the mechanical vibrations would still be perceived like sound through the players physical contact with the mouthpiece and reed.

Did Backus actually say that the mouthpiece will not vibrate unless the reed hits the tip?
I know from my own experiments that with a large enough tip opening (or soft enough playing) the reed will not hit the mpc tip (confirmed by a dot of paint on the mpc tip not being picked up by the reed), yet the mpc still seems to vibrate.
Backus said this

http://iwk.mdw.ac.at/lit_db_iwk/download.php?id=9499

Backus's further research reveals that the instrument's body vibrations are due to the reed vibrating against the mouthpiece, not due to the vibrations of the enclosed air column.

In a 1964 experiment, University of Southern California physicist Dr. John Backus attempted to determine the role of a clarinet's body vibrations in sound production.5 Backus's experiment centered on a clever and slightly comical gadget, with an artificial embouchure powered by a household vacuum cleaner. The clarinet's tone holes were all closed (simulating a clarinetist playing the instrument's lowest note), and the bell of the instrument was fitted with a muting device. When the clarinet was "played" via vacuum cleaner in this way, no sound waves could pass from the air column inside the clarinet directly into the air surrounding the instrument. Backus found that in this situation the instrument was virtually silent; the vibrating wood of the clarinet emitted such weak sound waves as to be inaudible to a human ear at a distance of one inch from the instrument's body. Backus concluded that the wall vibrations of a clarinet are too small to produce a perceptible sound. Further, he speculated that if it were possible to make the instrument vibrate sufficiently to be heard, the consequence would not likely be a pleasant one; he pointed out that a similar phenomenon occurs when one of the instrument's keys works loose and causes an annoying buzz. Backus's further research reveals that the instrument's body vibrations are due to the reed vibrating against the mouthpiece, not due to the vibrations of the enclosed air column.
 

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Discussion Starter · #82 ·
Even if the reed doesn't hit the tip of the mouthpiece, it is still slapping against the rails.

The vibrations caused mostly by the reed slapping against the mouthpiece rails has what possible effect on the standing wave?

As I've already said, the player is sensing these mouthpiece vibrations orally and if these vibrations are in the micron zone it's quite possible that they can be sensed by the player and thought to be much bigger then they really are.

Even in the mouthpiece/neck area, the ratio of air molecule movement to mouthpiece/neck wall vibration movement is still dominated by the size of the air molecule movement of the standing wave.

For the wall vibrations to alter the standing wave in a noticeable way, might require pretty large wall vibration movement and it would probably cause sonic distortion effects as well.
 

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The wiki Clarinet model is pretty easy to understand for anyone that doesn't know anything about standing waves or what is happening inside the instrument.

The Sax is a bit different to the Clarinet but also very similar.

I thought I'd throw it in.
I would not dispute the science of what is going on, but there is something wrong with the way it is explained there as it seems to make no sense.

Basically it says the reed vibration cycle is cause by the air pressure in side being lower than that outside. As the air pressure inside the instrument starts off the same, in order for it to be lower than that outside, air would actually need to be sucked out of the mouthpiece, not merely blown in to it via a tiny hole.

Obviously this is wrong so what am I missing in that Wikipedia explanation, albeit that it's in regard to a clarinet?

This is the problem with being fascinated by how such stuff works, but at the same time being not very scientifically minded.
 

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I would not dispute the science of what is going on, but there is something wrong with the way it is explained there as it seems to make no sense.

Basically it says the reed vibration cycle is cause by the air pressure in side being lower than that outside. As the air pressure inside the instrument starts off the same, in order for it to be lower than that outside, air would actually need to be sucked out of the mouthpiece, not merely blown in to it via a tiny hole.

Obviously this is wrong so what am I missing in that Wikipedia explanation, albeit that it's in regard to a clarinet?

This is the problem with being fascinated by how such stuff works, but at the same time being not very scientifically minded.
Moving air is always at a lower pressure than still air. It's called the Bernulli Principle. If you've ever seen the old vacuum cleaner sales trick where they set up a vacuum in the blower mode, point the hose up, and then suspend a small beach ball (I use a table tennis ball for in class demos) in the airstream, you've actually seen it in action. The ball is suspended by the blower force, but is "captured" within the moving airstream by the pressure of the still air surrounding the airstream. If the ball is light enough, you can even tilt the airstream sideways quite a bit and the ball will stay pretty well in place (the airstream loses velocity quite quickly as it flares out from the hose, so the is even external still air pressure holding the ball relatively close to the hose.
 

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As to vibration of the beak increasing the compliance, we are talking in the range of a micrometer or two, maximum. Add two microns to the effective tip opening and tell me if you really think that makes a perceptible difference.

The thickness of the mpc walls is far greater than those of the body--by at least an order of magnitude, thus even commonly used materials of relatively lesser density are not going to deflect much in the presence of mechanical forces of the reed. This could easily be quantified.

While the reed is the generator of the standing wave, I'm a bit puzzled by your assertion that a vibration there makes more difference than anywhere else, especially because such vibrations in any case are minuscule. A good example of gross vibrational differences at the reed, of course, have to do with the mechanical properties of the reed itself, but the movements of the reed are thousands of times greater than those of the mouthpiece, so one has to put these in perspective. The baffle functions aeroacoustically to determine the speed of reed closure as it approaches the tip via Bernoulli forces. It does not "absorb" anything, unless you consider viscous losses at the boundary layer, which are dependent only on the smoothness of the walls.

It is really necessary to think in quantities. When you jump you actually push the earth in the opposite direction. How much do you think you deflect it, compared to your deflection?

This paper has some juicy parts about behavior at the mpc, mostly relevant also to sax:

http://hal.archives-ouvertes.fr/docs/00/25/27/96/PDF/ajp-jp4199404C5120.pdf

In any case I defer to Phil Barone, who reports no difference based on material if internal dimensions are the same--of course this could simply be a marketing tactic to sell cheaper mouthpieces ;-)
 

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Basically it says the reed vibration cycle is cause by the air pressure in side being lower than that outside. As the air pressure inside the instrument starts off the same, in order for it to be lower than that outside, air would actually need to be sucked out of the mouthpiece, not merely blown in to it via a tiny hole.
Do you have the Backus book? (Acoustic Foundations in Music. p218)
 

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Discussion Starter · #88 · (Edited)

When relaxed, the reed of a woodwind instruments is open.

When you blow past the reed into the instrument, why doesn't the air just go straight through?

Why does the reed close?

Moving air sucks, that's the Bernoulli principle.

The reed is sucked closed, but when closed there is no Bernoulli effect, so it opens up to then get sucked closed again…

The vibration of the reed is driven by pressure in the air column:

When a low pressure reaches the reed, the reed is sucked closed and the pressure cannot equilibrate to the outside pressure.

When a high pressure reaches the reed, the reed is pushed open and a puff of high pressure air is blown in.

Again, the pressure cannot equilibrate to the outside pressure.

Because the air column cannot come to equilibrium at the reed end, that end acts somewhat like a closed end.

The vibration of the reed is driven by flow of air in the column:

When high pressure reaches the end of the air column (first open tonehole, effective end), a stream of air is blown away from the opening, and air flows out of column.

When low pressure reaches the end of the air column, a stream of air is pulled into the opening, and air flows into the air column.
 

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The reed cycle of a sax is rather complex, much more than with a clarinet, in which the reed is open 50%/closed 50% of the time. In a conical woodwind the reed is reopened by a reflection from the end of the neck, so it spends most of its time open. Contrary to what some others have said here, the sax reed "beats" (closes the tip) most of the time, whereas in the clarinet it does so only at louder dynamics.

A high baffle increases Bernoulli forces as the reed closes, causing it to accelerate and snap closed when it approaches the tip. This changes the harmonic content of the sound, inhibiting lower harmonics.
 

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Discussion Starter · #90 ·
But wouldn't the amount of reed movement depend on the pressure and the stiffness of the reed and the mouthpiece tip opening/rails?
 

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Moving air is always at a lower pressure than still air. It's called the Bernulli Principle. If you've ever seen the old vacuum cleaner sales trick where they set up a vacuum in the blower mode, point the hose up, and then suspend a small beach ball (I use a table tennis ball for in class demos) in the airstream, you've actually seen it in action. The ball is suspended by the blower force, but is "captured" within the moving airstream by the pressure of the still air surrounding the airstream. If the ball is light enough, you can even tilt the airstream sideways quite a bit and the ball will stay pretty well in place (the airstream loses velocity quite quickly as it flares out from the hose, so the is even external still air pressure holding the ball relatively close to the hose.
Thanks, that makes sense to me. A least, I think I understand it anyway.
 

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As to vibration of the beak increasing the compliance, we are talking in the range of a micrometer or two, maximum.
This assertion is based on what research? I would sincerely love to see any study anybody has ever done to measure this. Or have you calculated it? If you have please share, because I can't figure out how to calculate the stiffness of a body with the shape of a mouthpiece.

If you're just guessing, OK, I'm guessing that you understimate it for some materials. I suspect that you're in the right neighborhood for the metals we use, but ebonite is more flexible, and delrin much more flexible and springy still.

In any case I'm just suggesting a physical model to explain the results I found last year (that there is a 99% chance that professional musicians can tell the difference between two otherwise identical mouthpieces of different materials 4.6 +/- .52 times out of 8).

It's not as if we need to keep speculating on this, we can just get a camera and look, but that will take a little time and money.
 

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Three sincere questions:
1- Where does the air column exactly start? Are we sure the beak/reed system is included?
2- I am struggling to thing of the behaviour of the walls vs the vibrating air column at a precise point of the body, for example at half the neck.
I am assuming there will be a high pressure moment followed by a low pressure moment, according with the note being produced, but we are talking about harmonics too. I would love to figure out the system under this reference point.
3- Are we sure that the only thing that makes the saxophone body vibrate is the air column? No direct movement through reed/ligature/body?
 

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Discussion Starter · #94 ·
The trouble with Science sometimes is that it's not that easy to get a picture of complex things especially if you are visually prone.

I think the UNSW Acoustic department should consider doing some visual animated demos for people to see what happens.

I'm not an expert in Acoustics so I can only try to give a rough picture that might not always be right and I stand to be corrected about anything I say.

As I understand it, the physical behaviour of the air column can be different for different frequencies depending on the inherent cutoff frequency of the Sax which is mostly due to the open toneholes forming a filter.

The vibrating air column has many different frequency components ie fundamental and overtones.

Loosely put, the air column extends to just past the first open tonehole for lower frequencies below the cutoff and of course if the vibrating air column is shorter then it sounds higher, so the high notes of the Sax have more open toneholes happening then the low notes.

The octave key disturbs the fundamental of the vibrating air column and the pitch therefore goes up to the next harmonic an octave higher.

Some higher frequency parts of the vibrating air column that are above the cutoff frequency can extend way past the first open tonehole and go straight out the bell and these are sometimes used in Altissimo and cross fingerings.
 

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I think my question number 2 wasn't clear.
If I play a B third line on a tenor, I will have a situation in an x point (that I conventionally placed somewhere on the neck) that will reproduce itself every 1/220 seconds. I cannot figure out (no need to be visual, I can read a list of numbers too) what happens, in that time, to the walls in terms of pressure.
 

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Discussion Starter · #96 · (Edited)
That B note has a lot of open toneholes, so the main part of the vibrating air column is extending from the beginning of the mouthpiece to just past the B key but higher frequency components of the B note are extending way beyond the B key.

The pressure is the same bernoulli effect and first open tonehole situation explained above.

"When high pressure reaches the end of the air column (first open tonehole, effective end), a stream of air is blown away from the opening, and air flows out of column.

When low pressure reaches the end of the air column, a stream of air is pulled into the opening, and air flows into the air column."

It isn't a huge pressure so it doesn't deform the Sax walls much at all.

If no one is blowing into a Sax then the pressure inside the Sax is at the outside pressure, the same as outside the Sax.

A small pressure change by the player induces counter pressures inside the Sax and the pressure inside the Sax wants to get to the outside pressure but can't because of the players induced pressure causing corresponding reed pressure changes and also the Sax's first open tonehole pressure changes, so it's a bit like a ping pong pressure effect while the note is being played between the reed and the first open tonehole.

As the pressure changes near the open tonehole and air is blown out or sucked in of the tonehole (depending on pressure), then things connected with the tonehole can have an influence of the vibrating air length, such as the keys.

If the keys are closer to the toneholes then they can affect the length of the vibrating air column and therefore intonation, because the keys are in the path of the blown out/sucked in air around the tonehole.

The toneholes have edges that might interfere with the formation of the vibrating air column especially near the first open tonehole.

The effect of the reed and vibrations was gone into in some of the posts above.

For a lot of people, things like this shown in an animated video would be of help in understanding some of it IMO.
 

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Three sincere questions:
1- Where does the air column exactly start? Are we sure the beak/reed system is included?
2- I am struggling to thing of the behaviour of the walls vs the vibrating air column at a precise point of the body, for example at half the neck.
I am assuming there will be a high pressure moment followed by a low pressure moment, according with the note being produced, but we are talking about harmonics too. I would love to figure out the system under this reference point.
3- Are we sure that the only thing that makes the saxophone body vibrate is the air column? No direct movement through reed/ligature/body?
1-- yes, we're sure the reed (and IMO if it moves, the beak) is included. Somewhere around the tip of the reed is a pressure antinode, the end of the tube is a pressure node, the standing wave is between these two points.
2-- I'm assuming that to the extent that the tube does vibrate, it does so parallel to the air column that it bounds, with nodes and antinodes in the same place. So not moments, but regions, of high and low pressure. A 2-d cross-section of it on the y-z plane would look just like the waveform of the sound played.
3-- no, we're not (at least I'm not).
 

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So not moments, but regions, of high and low pressure. A 2-d cross-section of it on the y-z plane would look just like the waveform of the sound played.
Finally on the way! And thank you for not answering with a link.

I am trying to refer to moments, not regions. I apologize for my poor control of the idiom, but some sort of pressurimeter applied in one point before the relevant tone hole should show the variations of pressure in that 1/220 sec.
I am not sure the shape of the wave will be the same of the sound played. Same frequency yes, same shape maybe.

About the first question, I trust your opinion, while my feel was more of a hell of turbolence going on there, stabilizing at some point in the bore.
 

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Discussion Starter · #100 ·
The standing wave forms between the mouthpiece's (effectively closed pipe end) (pressure antinode) and the first open tonehole (effectively open pipe end) (pressure node) but it extends beyond the first open tonehole for frequency components of the standing wave that are above the cutoff frequency, because these higher frequency components don't see the open tonehole as an open pipe end whereas the frequency components below the cutoff frequency do see the open tonehole as an open pipe end.

For frequency components below the cutoff frequency,

If you open the tone holes, starting from the far end, you make the pressure node move up the pipe, closer to the mouthpiece---it is very much like making the pipe shorter. Starting near the bell, each opened tone hole raises the pitch by a semitone, which requires a pipe that is about 6% shorter. After you open all of the right hand finger holes, as shown below, you have the fingering for G4, which is shown here http://www.phys.unsw.edu.au/jw/saxacoustics.html#toneholes

The pressures involved are not that much, so if someone is looking for significant wall deformations caused by the pressure then that has already been researched and from what I've read, it isn't much.

The Sax isn't a pressure cooker.

The saxophone player provides a flow of air at a pressure above that of the atmosphere (technically, a few kPa or a few percent of an atmosphere: applied to a water manometer, this pressure would support about a 30 cm height difference). This is the source of power input to the instrument, but it is a source of continuous rather than vibratory power. In a useful analogy with electricity, it is like DC electrical power. Sound is produced by an oscillating motion or air flow (like AC electricity). In the saxophone, the reed acts like an oscillating valve (technically, a control oscillator). The reed, in cooperation with the resonances in the air in the instrument, produces an oscillating component of both flow and pressure. Once the air in the saxophone is vibrating, some of the energy is radiated as sound out of the bell and any open holes. A much greater amount of energy is lost as a sort of friction (viscous loss) with the wall. In a sustained note, this energy is replaced by energy put in by the player. The column of air in the saxophone vibrates much more easily at some frequencies than at others (i.e. it resonates at certain frequencies). These resonances largely determine the playing frequency and thus the pitch, and the player in effect chooses the desired resonances by suitable combinations of keys.
 
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