Tech/maintenance Saxophone Pad Acoustics Study

[saxyjt]

Phil in the video above is not spitting flames, but abadcliche is promising bigger and more dangerous, so I'm only guessing!

 

[Dave McLaughlin]

So there are areas inside the saxophone that have, at least for a short amount of time, lower pressure than atmospheric?

At the risk of taking this out of graduate thesis pdfs and into the physical world, how much like what goes on inside the saxophone is the video below of standing waves in a wave tank? AFAIK: In a saxophone, you've got waves of high and low pressure coming from the mouthpiece that bounce off the atmosphere at the first open tonehole (or bell) and travel back up. By figuring out how much volume and length to have inside the tube, you can set up standing waves- which is where the outward and inward waves repeatedly intersect at the same spot, roughly doubling their amplitude in certain static spots. Which looks like what I see here, but I don't know how much of this to take and use for my mental picture.

It's very much like that. When the water is high, that causes an increase in pressure under it. When a standing wave pattern is set up, the wave height at the antinodes varies between a maximum (above the level of the undisturbed water) and a minimum (below the undisturbed level). The water at those antinodes moves up and down, but not along the length of the pool, so they represent nodes in the horizontal velocity. In between those height/pressure antinodes are height/pressure nodes, where the height does not vary, but the horizontal velocity fluctuates as water moves between the height/pressure antinodes on either side.

 

[jbtsax]

Not quite. Zero pressure would be a vacuum. At a pressure node, there is zero fluctuating pressure.

Thank you for that correction, I was in too much of a hurry. Another way to say that is at a pressure node there is no change in pressure.

At a pressure antinode, there is the maximum pressure fluctuation. But it fluctuates, plus and minus, about atmospheric pressure.

Now that you mention it, I may have been thinking about this the wrong way. In the sound wave there are, in fact, areas of compression where the air molecules are pressed together and areas of rarefaction where the air molecules become spread apart. That raises the question of how significant these periods of slightly below atmospheric pressure are inside a woodwind.

Since this thread has taken a different direction, I will only post again when the data is in and the study is complete.

 

[Jobe]

This is interesting science, and thanks for posting this technical study!

 

[kevgermany]

That raises the question of how significant these periods of slightly below atmospheric pressure are inside a woodwind.

Given that zero is treated as the pressure at the openings - i.e. atmospheric, and that at the pressure antinodes there's higher than atmospheric pressure, does it really drop below atmospheric? Or does the pressure inside vary from a lower limit of atmospheric pressure upwards?

In any case, if a pad is porous, you'll get transmission through the pad in both directions, into the pad as pressure increases and out of the pad as it decreases.

I'm not sure if under steady state (e.g. blowing a continuous note) pressure at a pressure antinode varies. I'd have though it only changed when the position of the antinode moved as the player changes the note.

 

[Dave McLaughlin]

Given that zero is treated as the pressure at the openings - i.e. atmospheric, and that at the pressure antinodes there's higher than atmospheric pressure, does it really drop below atmospheric? Or does the pressure inside vary from a lower limit of atmospheric pressure upwards?

Do you agree that sound in general involves both positive and negative pressure variations around atmospheric pressure? Take a loudspeaker, for instance. When the diaphragm moves forward from its middle position, it compresses the air in front of it to higher than atmospheric pressure. When it moves back from the middle position, it stretches the air in front of it to lower than atmospheric.

You're right that the pressure at the openings is very nearly zero. You know that the standing wave field can be thought of as two superimposed travelling waves, travelling in opposite directions? And you know that the pressure in a travelling wave fluctuates between a maximum and a minimum? The only way those two waves can add to give a constant value of zero at the first open tone hole is if the pressure of the reflected wave is always the negative of the pressure of the incident wave.

In any case, if a pad is porous, you'll get transmission through the pad in both directions, into the pad as pressure increases and out of the pad as it decreases.

Agreed.

I'm not sure if under steady state (e.g. blowing a continuous note) pressure at a pressure antinode varies. I'd have though it only changed when the position of the antinode moved as the player changes the note.

This reminds me of a discussion we had a while back. I always felt vaguely guilty that I got distracted and left that unfinished. The saxophone is complicated, because it's conical, but consider a clarinet. It's a cylinder, open at one end, and almost closed at the reed. (You know that playing a reed instrument involves blowing a relatively small volume of air at high pressure, unlike a flute, which involves blowing a lot of volume at low pressure. That's because the reed instrument is essentially closed at the reed, whereas the flute is open.)

At a closed end, the fluctuating velocities of the two propagating waves must add to zero, because the end can't move. That means when the fluctuating velocity of the incident wave is at a positive maximum (in its direction of travel), the fluctuating velocity of the reflected wave must also be at a positive maximum in its direction of travel (because it's travelling in the opposite direction). And because the fluctuating pressure in a travelling wave is in phase with the fluctuating velocity (and pressure is a scalar, not a vector, so they add), the pressure at a pressure antinode fluctuates between a maximum and a minimum.

Hmm - reading over this, I can see it's not very satisfactory and may be difficult to follow. I can try to find a way of showing this graphically for those who aren't familiar with the maths. For those who are familiar with the maths, I could put together some formulae. If anybody's interested, would you prefer sines and cosines or complex exponentials?

 

[Dave McLaughlin]

Apologies, jbtsax - it occurred to me I'd never actually indicated that I liked your original post. I just went to do so and was horrified to find I'd somehow inadvertently tagged it as "Funny". You must have thought me very rude.

 

[jbtsax]

Just a quick update. Dr. Pauline Eveno has received the pads sent to Paris, and has indicated she can conduct the tests sometime in August.

It is common nowadays for techs to check woodwind pads for leakage at various pressure levels using the Magnehelic machine. This raises an interesting question: How much "acoustic sound pressure" is actually inside a woodwind instrument that pushes against the keys when played at its loudest levels? None of my searches have turned up any information in the acoustic information available online.

One source did refer to pressures a high as 175 db inside of a trumpet which equals 11246.8 pa (pascals) which would represent 45" h2o on a magnehelic if the gauge went that high. Dr. Gary Scavone is quoted as saying that 2000 pa is the number tossed around a lot for the pressures inside a sax mouthpiece. That would represent 8.3" h2o or 165 db. Obviously as the sound waves leave the mouthpiece and go into an increasingly wider tube, the pressure levels will decrease.

Upon Dave McLaughlin's recommendation I have purchased the micW i436 calibrated measurement microphone and the Analyzer app for the ipad. While we are waiting for the results of the acoustic absorption tests, my assistant Jory Woodis and I will be taking measurements of the acoustic sound pressure levels inside a saxophone being played at its loudest levels. Hopefully we will be able to come up with some accurate and repeatable data on this fascinating subject.

 

[Dave McLaughlin]

Upon Dave McLaughlin's recommendation I have purchased the micW i436 calibrated measurement microphone and the Analyzer app for the ipad. While we are waiting for the results of the acoustic absorption tests, my assistant Jory Woodis and I will be taking measurements of the acoustic sound pressure levels inside a saxophone being played at its loudest levels. Hopefully we will be able to come up with some accurate and repeatable data on this fascinating subject.

I hope the microphone lives up to expectations. The software looks quite good, and if it doesn't do quite what you want, it can export *.csv files which you can then read into any spreadsheet for additional manipulation.

Don't be too disheartened if the repeatability isn't as good as you at first expect. A difference of 1 or 2 dB is just niticeable.

 

[jbtsax]

The first tests with the microphone inside the saxophone were not successful. The dB spl apparently was above the limits of the microphone and "clipping" occurred. Fortunately they make a 20 dB attenuator that goes with the microphone. We tested the mic with the inline attenuator and it worked perfectly. @Dave McLaughlin can correct me if I am wrong, but the readings on the Analyzer app are then increased by 20 dB to get the correct sound pressure level.

Exact measurements of each note and position inside the saxophone will be charted eventually, but the initial finding is that the sound level does not exceed the level of 130 dB which is the new limit of the mic with the attenuator. Techs typically measure the leakage of pads using up to 8 inches of water pressure on the magnahelic pictured in the first post in this thread. Interestingly enough 130 dB is the equivalent of .25 in. H20 which represents close to the maximum pressure inside a saxophone.

Dr. Eveno has been working on the acoustic absorption tests in Paris and hopefully there will be some data soon to compare with the porosity measurements of the pads. Stay tuned.

 

[aldevis]

Exact measurements of each note and position inside the saxophone will be charted eventually, but the initial finding is that the sound level does not exceed the level of 130 dB which is the new limit of the mic with the attenuator. Techs typically measure the leakage of pads using up to 8 inches of water pressure on the magnahelic pictured in the first post in this thread. Interestingly enough 130 dB is the equivalent of .25 in. H20 which represents close to the maximum pressure inside a saxophone.

Help!
How would it be in millibars?
I am struggling to find a usable relation betweem dB and bars.
If there is no wave in a saxophone, internal pressure should be 1 bar (assuming 1000 mBar of atmospheric pressure). When it start moving, how much is the pressure changing at its maximum (and minimum)?

 

[jbtsax]

First of all please remember that I am not an acoustic scientist (although I play one on the internet). 🙂

Here are some figures from my research:

The standard atmosphere (symbol: atm) is a unit of pressure equal to 101325 Pascals or 1013.25 hectopascals (millibars) equivalent to 760 mmHg (torr), 29.92 inH20, 14.696 psi. However standard atmospheric pressure is simply the starting point or baseline. In acoustics it is the pressures above (or below) atmospheric pressure that are significant inside the instrument in my understanding.

1 Pa = .01 mb = .004 in H20 = 93.98 dB

8 in H20 = 1992.656 pa = 160.0 dbspl = 19.93 mbar
4 in H20 = 996.328 pa = 153.9 dbspl = 9.96 mbar
2 in H20 = 498.164 pa = 147.9 dbspl = 4.98 mbar
1 in H20 = 249.082 pa = 141.9 dbspl = 2.49 mbar
.5 in H20 = 124.540 pa = 135.9 dbspl = 1.24 mbar
.25 in H20 = 62.270 pa = 129.9 dbspl = .62 mbar

 

[aldevis]

And in which ballpark are we dancing when we look at the pressure of the standing wave against the pad/saxophone wall?

 

[Dave McLaughlin]

The first tests with the microphone inside the saxophone were not successful. The dB spl apparently was above the limits of the microphone and "clipping" occurred. Fortunately they make a 20 dB attenuator that goes with the microphone. We tested the mic with the inline attenuator and it worked perfectly. @Dave McLaughlin can correct me if I am wrong, but the readings on the Analyzer app are then increased by 20 dB to get the correct sound pressure level.

Exact measurements of each note and position inside the saxophone will be charted eventually, but the initial finding is that the sound level does not exceed the level of 130 dB which is the new limit of the mic with the attenuator.

I'm glad that's working for you. If the software knows that the attenuator is there, then it should be able to correct for it, otherwise you'd have to add 20 dB yourself.

 

[Dave McLaughlin]

8 in H20 = 1992.656 pa = 160.0 dbspl = 19.93 mbar
4 in H20 = 996.328 pa = 153.9 dbspl = 9.96 mbar
2 in H20 = 498.164 pa = 147.9 dbspl = 4.98 mbar
1 in H20 = 249.082 pa = 141.9 dbspl = 2.49 mbar
.5 in H20 = 124.540 pa = 135.9 dbspl = 1.24 mbar
.25 in H20 = 62.270 pa = 129.9 dbspl = .62 mbar

Those look about right to me. One slight niggle is that dB levels are usually averaged over time, using root-mean-square (rms) averaging. The peak sound power will usually be higher than the rms. For a pure tone, with no harmonics, the difference between the two is 3 dB. For a brighter tone, with more harmonics, the difference could be higher. That would mean clipping could occur at lower rms levels.

 

[aldevis]

And in which ballpark are we dancing when we look at the pressure of the standing wave against the pad/saxophone wall?

Did I get right that 100dB are almost no pressure difference?

 

[jbtsax]

And in which ballpark are we dancing when we look at the pressure of the standing wave against the pad/saxophone wall?

From my initial testing with the attenuator attached the maximum dB levels were somewhere in the 120's. We could not make them exceed 130 dB which is the upper limit of the mic according to the manufacturer. Standing near the source, 130 dB would be a painfully loud level so its best not to put a sax mouthpiece up to someone's ear and blow as loud as you can. 🙂

I just saw your second question. It is important to remember that all of these measurements are above and beyond normal atmospheric pressure which we humans have no sensation of.

 

[Dave McLaughlin]

Did I get right that 100dB are almost no pressure difference?

I think the important thing to appreciate is that the human ear is almost incredibly sensitive. The minimum perceptible pressure difference is notionally 20 micropascals or 20 millionths of a Pascal*. Standard atmospheric pressure of 1 bar is 100,000 Pascals, so the minimum perceptible is 0.2 billionths of atmospheric pressure. 100 dB would be a pressure difference of 100,000 times 20 micropascals, so quite a lot higher than the minimum perceptible. But it's still only 2 Pascals, or 2/100,000 of atmospheric pressure. So on a scale of atmospheric pressure, it's almost nothing, but on a scale of human hearing, it's a helluva lot.

*Exposure to loud sounds can seriously damage your hearing, and the 20 micropascals is really only perceptible by young children whose hearing hasn't been damaged by exposure to loud sounds. If you play a saxophone for more than a few minutes a day, you should consider wearing ear protection.

 

[aldevis]

I am now thinking in terms of pressure against a pad.
Not the forthcoming Otopads™ made from real ears.
It seems to mean that 100 dB is about like gently blowing to move a cigarette paper on the table.

 

[Dave McLaughlin]

It seems to mean that 100 dB is about like gently blowing to move a cigarette paper on the table.

Yes, 2 Pa or 2 Newtons per square metre is a tiny pressure. You can refer to jbtsax's post to convert that to other units.