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High Range via Resonant Vortex Shedding



 
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etc-etc
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PostPosted: Fri Jan 08, 2021 12:00 am    Post subject: High Range via Resonant Vortex Shedding Reply with quote

In the video below, James Morrison attributes the pitch played by the trumpeter to the speed of air: fast air causes high notes, and slow air causes low notes. James Morrison says that a wider open embouchure causes a high volume of sound, and a more narrowly open embouchure causes a low volume of sound.


Link


The question is, by virtue of what physical mechanism would a higher air speed translate into a higher vibrational frequency of the trumpet?

I propose that this mechanism is a combination of turbulent vortex shedding and aeroelastic flutter.

Air speeds up to 100 m/s can be produced at the aperture of a trumpet or flute player playing at a maximum lung pressure:
JW wrote:

Now consider a location with low cross section, say a tenth of a square centimeter (= 10−5 m2). Such a value is possible for the lip aperture of a flutist, between a trumpetter's lips, or between a clarinet reed and mouthpiece.
...
Combine our range of flows (0.1 to 1 litres per second) and apertures (0.1 to 10 square centimetres): this tells us that the air speed will usually be in the range 0.1 m/s (a wide area of the mouth or throat with soft playing) to 100 m/s (for loud playing and a narrow aperture). It's worth repeating that dependence on aperture cross section: the average flow rate could simultaneously be 1 m/s in a flutist's throat and 100 m/s where it leaves the lips.

https://newt.phys.unsw.edu.au/jw/air-speed.html


Under high air speeds, turbulent oscillatory behavior (aeroelastic flutter) can develop:


Link


Consider turbulent vortex shedding in fluid flowing around a cylinder of a diameter D:

Image by Cesareo de La Rosa Siqueira posted originally on https://en.wikipedia.org/wiki/Vortex_shedding

The frequency f of vortex shedding is directly proportional to the speed V of the fluid (in our case, air):

f = St * V / D

where St is the dimensionless Strouhal number (for a wide range of Reynolds numbers and geometries St is between 0.1 and 0.3): https://www.sciencedirect.com/topics/engineering/strouhal-number .
Let us estimate St = 0.22 .

The equation above can be re-written to find the air speed V needed to produce a note of frequency f:

V = D * f / St

As the geometry of the lip reed is quite different from the geometry of fluid flowing around the cylinder, consider D to be the size parameter (multiplied by an adjustment coefficient due to geometry of the lip reed). Let us estimate D = 0.003 m.

For the high C on a Bb trumpet (equivalent to Bb5), f = 932.33 Hz:
https://pages.mtu.edu/~suits/notefreqs.html

Then, V = 0.003 [m] * 932.33 [1/s] / 0.22 = 12.7 m/s, which is much less than the maximum air speed of 100 m/s estimated in https://newt.phys.unsw.edu.au/jw/air-speed.html

For a double high C on a Bb trumpet, f = 1864.66 Hz, and V = 25.4 m/s.
For a triple high C on a Bb trumpet, f = 3729.31 Hz, and V = 50.8 m/s.
For a quadruple high C on a Bb trumpet, f = 7458.62 Hz, and V = 101.6 m/s (close to the highest air speed estimated above).

This calculation validates, in principle, the mechanism by which the "fast air" can be indeed responsible for production of high notes on a trumpet. This explanation answers several questions:

1) Role of lung pressure - to supply the pressure differential needed to sustain the desired air speed.
2) Role of lip compression - to establish a narrow embouchure that will allow to attain the desired air speed.
3) Role of embouchure pliability - to amplify the effect of vortex shedding (likely, by a mechanism similar to aeroelastic flutter) and allow the lip reed to rapidly open and close in sync with the shed vortexes.
4) Role of the embouchure support - flutter can lead to disintegration of the oscillator. If the embouchure is blown too wide open, sound will cease to be produced.

Having understood the principles of high note formation, one can now decide the practice regimen that will facilitate high range development:
1) work on increasing the lung pressure.
2) work on making the narrowest possible embouchure.
3) maintain the center of embouchure pliable to amplify the vortex shedding by flutter of the lip reed.
4) make sure that the embouchure is not blown open by the increased lung pressure.

A warning regarding high pressure playing:
JW wrote:
A warning for high-range trumpeters (...): sustained very high pressures are reported to affect circulation in the head and neck, with reports of possible consequences including stroke and eye damage. Be careful, and try to achieve the high range with embouchure rather that pressure (...).
https://newt.phys.unsw.edu.au/jw/air-speed.html


Finally, let us consider how does one control the loudness of the sound under the resonant vortex shedding. I propose that the loudness is controlled by the viscosity and elasticity of the embouchure muscle:
https://ouhsc.edu/bserdac/dthompso/web/namics/visco.htm#

According to https://pubmed.ncbi.nlm.nih.gov/9432095/ ,
wrote:
(...) well controlled isometric muscular contractions may result in decreased passive tension in a muscle at neutral length

Thus,
1) A tense embouchure will resist flutter and produce a small sound amplitude.
2) A relaxed/pliable/elastic embouchure will be prone to flutter and will produce a large sound amplitude.


Last edited by etc-etc on Fri Jan 08, 2021 1:26 am; edited 1 time in total
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deleted_user_687c31b
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PostPosted: Fri Jan 08, 2021 1:24 am    Post subject: Reply with quote

I'm not sure I quite understand how you connect 'flutter' to sound...are you implying that the speed of the air is what makes the mouthpiece vibrate because it starts an oscilliary motion? Or the lips?

There's one part of your reasoning I do not fully understand: the mass of the fluttering objects in the video you provide (the airfoils and the suspension bridge) is relatively low compared to the amount of air, in contrast to the mouthpiece (or even the whole trumpet) and the same goes for stiffness. It could apply to the player's lips I guess (and that can be verfified by imitating a horse's vibrating lips: the airstream clearly affects that) but I don't quite see how the two are connected. Maybe you could elaborate?
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etc-etc
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PostPosted: Fri Jan 08, 2021 1:31 am    Post subject: Reply with quote

hibidogrulez wrote:
I'm not sure I quite understand how you connect 'flutter' to sound...are you implying that the speed of the air is what makes the mouthpiece vibrate because it starts an oscilliary motion?

There's one potential flaw in your reasoning (maybe you can explain why it's not): the mass of the fluttering objects in the video you provide (the airfoils and the suspension bridge) is relatively low compared to the amount of air, in contrast to the mouthpiece (or even the whole trumpet) and the same goes for stiffness. It could apply to the player's lips I guess (and that can be verfified by imitating a horse's vibrating lips, the airstream does affect that) but given that the biggest part of the lips for said technique is quite rigid, I'm not quite sure I understand the connection. Maybe you could elaborate?


You are quite right that the mass and stiffness of the mouthpiece and of the trumpet are far too high to cause flutter with our breath. But we do not need to cause the flutter of the mouthpiece. The fluttering object is the lip reed with negligible mass and low stiffness.
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HERMOKIWI
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PostPosted: Fri Jan 08, 2021 5:38 am    Post subject: Reply with quote

The foundational premise is erroneous. Air speed has nothing to do with the pitch produced by a player playing a trumpet. Play a note, hold it and then increase the air speed and all that happens is that the note gets louder. Higher pitch is a function of the chop setting increasing resistance on the air stream combined with the vibration reaction of the chop setting to that increased resistance. Pitches don't change without a change in the chop setting. Those changes can be subtle but they are changes nonetheless.

As long as there is an adequate air supply you can produce any note on the trumpet without changing the air speed.
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JayKosta
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PostPosted: Fri Jan 08, 2021 8:45 am    Post subject: Reply with quote

It is NOT the air speed that controls the pitch.
BUT the process of adjusting the lips and embouchure to PRODUCE the feeling of controlling air speed DOES result in the lips being set to produce higher or lower pitches.

The suggestion to 'increase the air speed' can be successful in obtaining higher notes because of the lip adjustments needed to accomplish the feeling of increased air speed.

Similar lip adjustment changes can result from using tongue arch - it is not that the physical size, shape, position of the tongue makes a difference, but the muscle effort of adjusting the tongue also affect the lips and embouchure.
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Andy Del
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PostPosted: Fri Jan 08, 2021 11:23 am    Post subject: Reply with quote

Ah, while this is all nice to ponder on a quiet Saturday night, what does it achieve for a player? Zero. Zip.

The scholarly investigation into sound is NOT an investigation into how to play high notes on a trumpet. Seeing as you are quoting Joe (I know the people at UNSW) and some of the asides made in their website, you should have realised this.

cheers

Andy
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Bflatman
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PostPosted: Sat Jan 09, 2021 8:06 pm    Post subject: Reply with quote

When I speed up the air as I play the volume of the air that I blow into the mouthpiece increases and the volume goes up but the pitch remains the same.

It is all about control of the embouchure and control of the air.

I can play very softly with tiny amounts of air exhaled at low speed or loudly with huge amounts of air exhaled at high speed.

As the volume of air increases through the embouchure the speed must increase but pitch does not vary.
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