A Strange Hybrid Instrument

[Chris Ghent]

On 9/25/2019 at 1:42 AM, ttonon said:

I believe the method you chose to suppress high frequencies from the sound spectrum has theoretical backing.  As the tongue moves through its swing cycle, the pressure and aerodynamic forces on the tongue change very abruptly in both magnitude and character.  This is because the slot provides a very different environment from the free space above the slot.  In cases where the tongue passes completely through the slot, we have an additional region of free space, which is also significant.  The velocity of the tongue is zero at the extremes of motion, and it is maximum just about where it downwardly enters that slot.  Such a rapid change in forces is in mathematical terms a step function, and the representation of a step function by a Fourier series contains many higher harmonics.  So if you reduce the "suddenness" of the step function, you reduce the contribution by higher harmonics.

 

Hi Tom,

I expected rounded surfaces to be quieter in the higher freqs because of a couple of misspent but enjoyable years hangliding in the middle 70s. You develop a sense of the way wind moves around structures, what creates turbulence and also the noise made by different shapes.

 

I never thought the rounded surfaces would lower volume because I equated volume with quantity of airflow and the nature of the sides of the clearance  would not change that; as long as the clearance was the same I thought the volume would be. The perceived volume dropped because the higher partials now removed were discordant ones.  I have long thought (and some of your words are the first confirming ones I've read) that a reed will give best speed and volume when, as it moves down to the top of the slot, the entire slot is blocked off as much as possible at the same time. I create this effect by bending the set into the reed in exactly the place it will bend down under pressure. For this reason the simple, "adjust the reed until the tip is around its own thickness above the frame" is not just simple but simplistic. At the moment at which the reed lies perfectly flat at the top of the slot I think there is an instant of air compression (this, I think, is your water hammer moment, though water cannot compress)  followed by an explosion of air expansion as the reed moves down. (An aside, in the 70s I had a motorcycle tuning book called "Tuning for Speed", worth hundreds now, wish I could find it, and in it Phil Irving, designer of the Vincent, says, "compression is acceleration").  I don't see any reason why this would be lessened by rounded surfaces rather then square if the  frame/tongue clearance is the same. When I find the reeds (I made two), I will see if I can find a volume comparison but there would be many obstacles to a clean comparison with a square edged reed.

 

I never really did think the rounded edges in the frame and tongue might make the reed double action but as you say, worth a few seconds experiment. What I did think might work was creating a sinusoidal shape to the tongue. If the sides of the frame were similar top and bottom  ) (   and the reed snaked under the tight spot and then above it then the conditions might exist to start both ways. The downsides might be a lack of a definite compression point as above and slower starting when the part of the reed above the frame was at the root end of the tongue. I have also been thinking of those harmonium reeds in which the last 5 mms are twisted to a 45° angle. These might start both ways. Of course the inefficiency of such a reed only makes sense in the light of a large wind chest and a pair of pedals but just to check the principle it might be interesting.

 

To recap, I think we might be in agreement on the form of the slot except for whether  the nature of the compression point (square or rounded) might affect the volume in any way other than increased or decreased by the addition or subtraction of higher harmonics. I am always conscious Tom, your words might have a more precise meaning than mine in scientific terms so my apologies if I have misunderstood anything you have said. For my own errors I am, of course, sorry.

[alex_holden]

3 hours ago, Chris Ghent said:

I never thought the rounded surfaces would lower volume because I equated volume with quantity of airflow and the nature of the sides of the clearance  would not change that; as long as the clearance was the same I thought the volume would be. The perceived volume dropped because the higher partials now removed were discordant ones.  I have long thought (and some of your words are the first confirming ones I've read) that a reed will give best speed and volume when, as it moves down to the top of the slot, the entire slot is blocked off as much as possible at the same time. I create this effect by bending the set into the reed in exactly the place it will bend down under pressure. For this reason the simple, "adjust the reed until the tip is around its own thickness above the frame" is not just simple but simplistic. At the moment at which the reed lies perfectly flat at the top of the slot I think there is an instant of air compression (this, I think, is your water hammer moment, though water cannot compress)  followed by an explosion of air expansion as the reed moves down. (An aside, in the 70s I had a motorcycle tuning book called "Tuning for Speed", worth hundreds now, wish I could find it, and in it Phil Irving, designer of the Vincent, says, "compression is acceleration").  I don't see any reason why this would be lessened by rounded surfaces rather then square if the  frame/tongue clearance is the same. When I find the reeds (I made two), I will see if I can find a volume comparison but there would be many obstacles to a clean comparison with a square edged reed.

 

Hi Chris. I have come to the same conclusion about how to set a reed, however I disagree about volume coming only from the speed of air flow. My theory is that volume comes from the amplitude of the pressure pulses that happen due to the 'air hammer' effect at the instant the tongue blocks the slot. The biggest pulses will happen if both the air flow is high and the flow is interrupted as instantaneously as possible. If the top edges of the vent/bottom edges of the tongue are rounded, that would cause the flow to be interrupted more gradually, leading to a smaller pressure pulse. I also have some rough ideas about how the shape and size of the reed chamber effects the amplitude of the pressure pulses, though I have no idea how to mathematically model it.

[ttonon]

Hi Chris and Alex, a little more on what powers the vibration.  Until very recently, it was pretty much unknown just how the free reed worked, or how energy was extracted from the steady bellows pressure in order to maintain vibration.  I never saw any description of it in the scientific literature.  I wanted to apply principles of fluid mechanics to this problem and for that, I needed a physical model to describe the forces acting on the vibrating tongue, and it finally dawned on me that there is an important asymmetry in the up and down motion, and it’s that asymmetry that explains the crux of the issue. 

 

The tongue covers the top surface of the slot in traveling both upwards and downwards.  The important difference is that there’s a violent stoppage of airflow through the slot only during the downward motion.  In the upward motion, the tongue gradually shuts off air flow.  In downward motion, the airflow through the slot just before cutoff is high, up around a few hundred feet per second, several times higher than the tongue velocity in that location.  You can calculate this very simply from the steady flow Bernoulli equation for incompressible flow, and let me state a diversion: yes, I said “incompressible.”  It’s a well-known fact that air behaves as an incompressible fluid in flow situations when the Mach number squared is negligible with respect to unity, which is the case here.  So when I use the term “water hammer,” I’m being precise.  Water, in normal flow situations, can be considered incompressible, and for the air velocities associated with the free reed, air behaves like any other “incompressible” fluid. 

 

Getting back, in downward motion, the tongue suddenly stops the airflow, and as the air piles on, the kinetic energy of the air is converted to static pressure acting on the top of the tongue.  This static pressure is about equal to the pressure that cause the air flow to begin with, which is the bellows pressure, and that pressure adds to the bellows pressure which is already there.  We thus come to the important conclusion that the static pressure above the tongue at the moment of stoppage is about twice the bellows pressure. 

 

How long does that pressure act on the tongue?  It would be difficult to determine that precisely, however, we know that it decreases as the tongue moves further downward into the slot and as pressure waves move outward from the region.  The region of high pressure above the tongue expands and the pressure therefore drops.  We know the velocity of the tongue and we know that the pressure wave moving away from the region travels at the speed of sound.  But most importantly, the excessive pressure is acting in the same direction as the tongue motion.  It adds energy to the motion.

 

From all that, we can model the water hammer effect on the downward motion of the tongue.  What about when the tongue is moving upward?  In this case, 1) the stoppage of air flow is more gradual, thus any excessive pressure due to a water hammer effect will be less than in the case for downward movement of the tongue, and 2) any excess pressure caused by a stoppage of air is directed against the tongue motion. 

 

We thus uncover the secret for how the tongue vibrates, the mechanism by which a net bellows pressure energy is put into the motion.  In the downward tongue motion, the water hammer effect helps, or adds more energy to the tongue motion than during the tongue upward motion, when a smaller water hammer effect works against, or subtracts energy from the tongue motion. 

 

Using experimental data, I have been able to verify this description, which I have assembled into a physical model, and with which I have formulated a mathematical description.  I however do not have final numerical results to report here, and I’d prefer to first put it in publishable form.  For me, this is an ongoing project, and I’m able to spend time on it in a hit or miss fashion.  But I’ll keep you informed as I progress. 

 

Best regards,

Tom

[alex_holden]

Thanks Tom, that's interesting and fits in with how I have been thinking about it. I have been analogising it to the operation of a hydraulic ram pump. Water flow gradually builds up, then a valve suddenly shuts and the water in the pipe leading into the pump 'piles up' and generates a large pressure spike, enough to lift a packet of water to the top of a hill. Then the pressure dissipates and the spring-loaded valve is able to open again and restart the cycle. Comparing it to a reed, air flow through the chamber and wind slot gradually builds up, then the tongue suddenly blocks the flow and the air in the chamber piles up against it, giving the tongue a large downwards kick, enough to swing it further than static bellows pressure alone could. Where my mental model got a bit fuzzy is why isn't there also an air-hammer effect acting to prevent the upward swing; my guess was because during the downward half of the cycle the tongue is partially blocking the slot, the air flow doesn't build up as high. It makes sense that as you say, there is also a more gradual cutoff as the tongue swings back up and gradually enters the vent bevel.