Blowing machine

[david_h]

The 5kHz is in the right ballpark to be an open tube resonance in the calibrator. Back to pushing string?

Lots of small posts because I have been having trouble making this post all in one go for a couple of days - getting a server error

[Terry McGee]

When making the shhhh sound with the lips are we tuning noise or selectively amplifying/attenuating parts of it with a resonance in our mouths.

I'd say we are tuning noise by selectively amplifying/attenuating parts of it with a resonance in our mouths! But I imagine we're talking Helmholtz (volumetric) resonance, rather than our more familiar longitudinal whistle/flute resonances. As in Jaw Harp or the Ocarina body.

So unlike when we whistle with our lips there is no feedback to the jet.

And, particularly the shushhing into the whistle window reminds us how very important the jet-switching action is to our instruments. Just generating white noise and selecting small sections of it by tuning is never going to be heard in the pub!

[Terry McGee]

Maybe we are also selecting what gets to our ears from within.

You can easily check what's real by recording and playing back or even more interesting, by doing it into a spectrum analyser, eg the AutoTuner or a phone app.

[Terry McGee]

Now, I've been suffering from the Internal Server Error problem too, which is why I had to respond in two chunks. And even then had to resort to posting the first paragraph, and editing in the second. Couldn't get the third one up.

And couldn't seem to get the term "head cavitie"s through which is why I edited it out of your quote. I wonder if it will go now...

Seems alright now....

[david_h]

I'm guessing that the warbly effect suggests that at that point the two regimes are not in a simple harmonic relationship.

I had a look at the spectra across the first regime change when blowing just the head a week or so ago.(I did post something but decided it was out of step with the current focus so deleted it) In Audactiy, watching the spectrogram change with time, it looks like both spectra are present together for a while (maybe the jet is dithering between the two). The horrid noise could be beating between them.

Would the different end correction for the two pitches do that?

I also had a quick look at the change in spectrum within a regime. That the natural resonances of the tube are not (due to end corrections) exact multiples of the fundamental seems to come into play.

[Terry McGee]

It's interesting that only the Regime 1 to Regime 2 switch incurs a gap filled with Primal Chaos. The other regime changes involve hysteresis, so there is no gap.

[david_h]

I will have a look at the spectra with a tube on. The reason for experimenting with just the heads of my aged assemblage of whistles was that I need to get the sandpaper out to get most of the tubes back on.

[Tunborough]

Can you fill in data points between the top and bottom of each regime, please. The goal here is to be able to plot frequency as a function of air speed out of the windway, so enough points to show the shape of the curve. The low end of the first regime should be particularly interesting. The format you give above is good.

OK, how does this look? I've arbitrarily gone with a total of 5 points per regime, picking round numbers as they are easier to set on the Flow Gauge(s). And avoided going below 6 L/min as I thought we'd cast doubt on the accuracy any lower. But let me know if you'd like me to go lower and by how much (in flow or Hz terms).

That looks good, thanks.

Remember I warned you about Strouhal numbers? Well, here they are ...

A Strouhal number is a way to relate frequency to speed. For whistles, the interesting Strouhal number is:

St = f * Lw / v

where f is the fundamental frequency, Lw is the length of the window from windway exit to blade, and v is the air speed coming out of the windway.

Turns out, the top end of every regime on every whistle has a Strouhal number around 0.25. My earlier investigation put it around 0.26; it's around 0.23 in the numbers you got. St increases to the bottom of each regime, topping out around 0.5. The highest you got was St = 0.425 at the bottom of regime 1.

It would be interesting to see how far this goes by looking further at the low end of regime 1. The flow measurements may be uncertain, but we can still calculate velocity from the pressure measurements. Say 7, 6, 5, 4, and 3 mm H2O, if you can get measurable frequencies that low.

... and maybe a couple more points at the low end of regime 2, around 25 and 30 mm H2O.

[Terry McGee]

OK, updated figures...

Code: Select all

Feadog Mk1 with 243.6mm blade to end of tube, 7 April 2023			
Regime	Flow	Press	Hz
Bot 1	2	3	444
Lo 1	4.3	4	534
	5.8	5	585
	6.3	6	609
	6.7	7	621
	7	7.5	628
Med 1	9	13.5	641.1
Hi 1	10	17	645.2
Top 1	10.9	20	647
			
Bot 2	11.8	23	1242
Lo 2	12.3	25	1245
	13.4	30	1257
	14	34.5	1268
Med 2	17	48.5	1281.5
Hi 2	19	62	1290.5
Top 2	22	75	1296
			
Bot 3	17.6	52	1865
Lo 3	22	72	1899
Med 3	26	104	1916.5
Hi 3	30	143	1933
Top 3	34	182	1947
			
Bot 4	25.5	106	2505
Lo 4	30	140	2532
Med 4	36	201	2556
Hi 4	40	264	2575
Top 4	>40	370	2602

It is easier to set pressures than flows (given the dancing balls and even allowing for the poor resolution on the manometer), so it would be good if we can deal in pressures.

Note slightly changed figures for 5mm.

I noticed that when we got to the really low end, the tuning meter would suddenly drop to half the frequency, but then come back to the figures supplied above. It's pretty quiet sound. But if there are anomalies, that might be an issue we need to tease out.

It did occur to me that if we decided we could work in pressures rather than flows, we should experiment with feeding the Whistle Connector directly from the Pressure Regulator, doing away with the Resistor and the Flow Meters. I'd be interested to see if the more "low impedance" feed from the Pressure Meter influenced the Pressure changes we saw with the Calibrator and scraps of extra tubing.

We might though find that the direct feed would make setting the Pressure Regulator too touchy. The current arrangement does seem to let me set the Pressure reasonably easily.

[Tunborough]

Here's the other thing about the Strouhal number ... It is related to an acoustic property called impedance. [Aside: Note the "industrial collaborators" mentioned at the bottom of that page.]

To over-simplify, acoustic impedance resembles electrical impedance, which in turn is related to electrical resistance. Impedance has the form Z = R + iX, where Z is the impedance, R is resistance, and X is something called reactance. If we put energy (sound energy, in our case) into a system with this impedance, R represents the energy lost to the system. X represents energy that comes back to us, but shifted in time. It's pretty straightforward to calculate an acoustic impedance for a tube; it gets more complicated when we add toneholes and a whistle head, but not unmanageable. WIDesigner is built around a model to calculate acoustic impedances at the whistle window.

Plotting the Strouhal numbers from Terry's data against the ratio X/R that WIDesigner calculates for the frequencies gives a mostly straight line. The line starts around St = 0.23 for X/R = 0, and moves up as X/R gets more negative. (X is always zero or negative when the whistle is sounding, and R is always positive.) The data continues in a straight line, but flattens out as it rises above St = 0.4. It will be interesting to see if the plot looks the same for a different tube or a different whistle head.

Code: Select all

Feadog Mk1 with 244mm blade to end of tube, 4 April 2023
Regime	Flow	Press	Hz	v	X/R	Strouhal
Bot 1	2	3	444	5.81	-16.00	0.406
Lo 1	4.3	4	534	6.71	-13.00	0.423
	5.8	5	585	7.50	-8.50	0.415
	6.3	6	609	8.22	-5.21	0.394
	6.7	7	621	8.88	-3.56	0.372
	7	7.5	628	9.19	-2.60	0.364
Med 1	9	13.5	641.1	12.33	-0.81	0.277
Hi 1	10	17	645.2	13.84	-0.25	0.248
Top 1	10.9	20	647	15.01	0.00	0.229
Bot 2	11.8	23	1242	16.09	-4.45	0.411
Lo 2	12.3	25	1245	16.78	-4.20	0.395
	13.4	30	1257	18.38	-3.21	0.364
	14	34.5	1268	19.71	-2.31	0.342
Med 2	17	48.5	1281.5	23.37	-1.19	0.292
Hi 2	19	62	1290.5	26.42	-0.45	0.260
Top 2	22	75	1296	29.06	0.00	0.237
Bot 3	17.6	52	1865	24.20	-3.80	0.410
Lo 3	22	72	1899	28.47	-2.22	0.355
Med 3	26	104	1916.5	34.22	-1.41	0.298
Hi 3	30	143	1933	40.13	-0.65	0.256
Top 3	34	182	1947	45.27	0.00	0.229
Bot 4	25.5	106	2505	34.55	-2.95	0.386
Lo 4	30	140	2532	39.70	-2.13	0.339
Med 4	36	201	2556	47.57	-1.40	0.286
Hi 4	40	264	2575	54.52	-0.82	0.251
Top 4	>40	370	2602	64.55	0.00	0.214

[Tunborough]

It did occur to me that if we decided we could work in pressures rather than flows, we should experiment with feeding the Whistle Connector directly from the Pressure Regulator, doing away with the Resistor and the Flow Meters. I'd be interested to see if the more "low impedance" feed from the Pressure Meter influenced the Pressure changes we saw with the Calibrator and scraps of extra tubing.

We might though find that the direct feed would make setting the Pressure Regulator too touchy. The current arrangement does seem to let me set the Pressure reasonably easily.

Unfortunately, I can only calculate air speed from pressure when I have flow values for most of the pressures to confirm the relationship. The relationship for those numbers is a bit different than earlier measurements with the Feadog head with and without the Feadog tube.

[trill]

Unfortunately, I can only calculate air speed from pressure when I have flow values for most of the pressures to confirm the relationship. . .

but . . but . . . (nevermind)

[Terry McGee]

Unfortunately, I can only calculate air speed from pressure when I have flow values for most of the pressures to confirm the relationship. The relationship for those numbers is a bit different than earlier measurements with the Feadog head with and without the Feadog tube.

I guess that means the flowmeters stay.

I was a bit tickled by your query about the blade to end length, 243.6 vs 245.5. A variation of less than 1% when we're talking dancing beads and flickery manometers!

Let me know what you'd like next. There is still the shorter tube of the same diameter if that would tell us anything.

[trill]

. . . we're talking dancing beads . . . .

If I may ask: do they dance all the time ? Or only at the top of the range ?

[Tunborough]

Let me know what you'd like next. There is still the shorter tube of the same diameter if that would tell us anything.

Yes, the shorter tube on the Feadog head is the next place to look. Thanks.