Folded and unstuffed line measurements

[teodorom]

It appears that some of you built some TL (or ML-TQWT) having a folded line.
My problem is that in the scientific literature (Webster Horn Equation eventually applied to musical instruments, like trumpets and so on) it is often quoted that folding has effects on resonances, the fundamental and so on.
Translated in some other language it appears that Leff is dependent upon the frequency.
This can be disturbing in TL's and ML-TQWT's where the position of the driver (and the port) is critical.
Unfortunately until now I' haven't found (on the Net) anything quantitative (and predictive).
In order to understand the problem I need to correlate the physical design with the measurements (with the line unstuffed).
Any contribution ?
Thanks

[BillFitzmaurice]

As to the folding issue accepted practice with both TLs and folded horns is to take the measurement through the center of the pathway as the line/horn length. A more conservative approach is to measure along the shortest path possible,ie, to the inside of the bends. If anything this would make the line/horn longer than actually required for the desired Fp/Fh, but too long is usually a better way to go than too short.

As to the stuffed part of the equation, I suspect that you may be anticipating a major alteration in the line frequency when stuffed. Don't. Stuffing is mandatory to eliminate resonances above the Fp but it will not significantly lower the Fp.

[teodorom]

Yes, this is the standard answer that one could get among the DIY-ers.
But why there are people writing papers whose abstract is: <Some authors writing about brass musical instruments have used the term ''effective length,'' usually meaning the length of a cylindrical tube having the same resonance frequencies as a given horn, but possibly with different end conditions. In this paper, alternative definitions of effective length are considered, and one definition is chosen and generalized to all frequencies, not just discrete resonance frequencies. Within the framework of lossless plane-wave horn theory, a nonlinear first-order differential equation is derived that yields effective length as a function of frequency and horn contour. Effective length has been calculated for some horn contours resembling French horns and trumpets. The solutions are qualitatively consistent with the experience of instrument makers and players, and with the effective lengths of actual instruments, determined from measured resonance frequencies.> ?
http://scitation.aip.org/getabs/serv...cvips&gifs=yes
And please don't say that trumpets are not transmission lines: it's all about Webster !
I know that to get an aswer I shall need to make my own experiment or to buy that paper ...

[BillFitzmaurice]

Well. for one thing trumpets are not transmission lines; they are horns. They function identically to a horn speaker (which, not coincidentally, is why they are called horn speakers) in that at the small end sound is created by a transducer (mouthpiece), and the horn acts as an acoustical impedance transformer between the transducer and the air. A horn achieves gain throughout its passband due to this impedance matching function. A horn is a highly resonant device; since the horn is constantly expanding its resonant modes are fairly evenly distributed throughout its passband. A horn has wideband gain on the order of 10-15dB over the same transducer in a non-horn loaded configuration.

A transmission line is similar to a horn in that it uses a transducer and a (generally) quarter-wave length tube (relative to its lowermost passband frequency) but differs in that it does not achieve gain throught its passband. Transmission lines are also highly resonant devices, but unike a horn those resonances are not evenly distributed throughout its bandwidth. Stuffing is required to suppress all of the resonant modes save the one at the line frequency, otherwise response is very uneven. This stuffing also serves to damp out the transmission through the line of frequencies more than 1 octave or so above the line frequency, and the gain achieved by the line witihin this range over a driver mounted in a bass-reflex, for example, is usually on the order of 4-5dB.

The transmission line also differs from a horn in that with a transmission line one side of the driver cone is always exposed directly to the air, the other to the line. While a rear-loaded horn also exposes one side of the driver cone directly to the air and the other to the horn throat, a front loaded horn does not; one side of the driver (mouthpiece) is exposed to the horn, while the other side is contained by a chamber (your mouth).

[Nelson Pass]

Here's some data on a folded duct out of Beranek:

Note the wavelenth ratios which I take to be crossectional
dimensions, in this case, 1 foot.

[teodorom]

Horns, Transmission lines, ML-TQWT, Bass-Reflex (loudspeakers), wind and brass instruments (the other kind of horns), the human (and not only this one) mouth, the "strange" behaviour of some Cepheyds, ALL obeys to the same equation: the Webster Horn Equation (wich in turn is the specialization of the Euler and Hemholtz equations).
This equation can be handled by the two-port network (see Leach) method. This can lead to the SPICE analogy (starded by Leach and then anayzed in much finer detail by Putland.
MJK, on the other side, made the use of the two-port method much simpler (me, I like better his approach, because it is more "physical").
Unfortunately none of this authors analyzes in detail the behaviour of a folded line. On the other side Rienstra showed that Webster Horn Equation holds even on a folded line.
Since I don't have access tho the achademic literature ("only" to what is published on the Net), I'm a little bit lost.
Unfortunately it seems that the people of the DIY-ers rely only on some well established myth and no one has made any reliable measurement.

[BillFitzmaurice]

Here's some data on a folded duct out of Beranek:

Hi Nelson. I'm not sure if that's what the poster is trying to get at. Baranek's chart is predictive of the low-pass function of a folded pathway, while the poster seems to be more concerned as to the resonant mode effects that folding potentially creates. At least that's how I read it. I think he'd be set straight on the TL thing if he read George A's articles in AudioXpress, or saw how Joe came up with his Thor, but apparantly he doesn't have that as a source. He certainly wouldn't be able to fault Joe as far as measurements go, or George on the research side.

In any case, while Baranek's results are useful where folded horns with angular bends are concerned (though not those with round bends) I don't think it particulary applies with a folded TL, as one would not necessarily be concerned with the passage of frequencies more than an octave or so above Fp through the line anyway. But on the other hand if you are concerned with maximizing the LP function of the line it certainly shows that you want the bends tight, one of the points that Joe did make with Thor.

[Onur]

just for a comment I can say that the bends do effect the response of the TL design.

there are two parts of the travelling wave, real and imaginery. real part always represents the power radiated form the bend and the imaginary part represents the power reflected from the bend. The imaginary part effects on the cone movement and causes distorsion level to rise up. The same thing happens with the opening of the line to free space.

As I can not send big files (<500KB) please feel free to contact me to request a 3d simulation of the reflected waves (performed in a FEM software) both from an elbow and the opening.

My email is:
ilkorur@yildiz.edu.tr

[BillFitzmaurice]

The greatest potential for modes created specifically by the bend is going to arise from the distance across the combined path widths where the bend occurs. Assuming a 1 foot wide pathway that would give you a two foot distance from the outer wall to outer wall of the pathway at the bend, and that would give you a positive reflective mode at 282 Hz and a negative mode at 141 Hz. But a one foot wide pathway is very large; most TLs will have path widths far smaller, and therefore the modes will occur at higher frequencies where the stuffing can control them very easily.

As Nelson points out in another related thread this can be minimized further through the adoption of angled reflectors at the bends, which will scatter the reflective modes across a wide bandwidth rather than concentrating them at two frequencies, with an attendant smoothing of response. I'd say the main advantage to angled reflectors would be where the pathway is wide and the amount of stuffing required to damp out the resulting modes at low frequencies would be excessive.

The power reflected back to the cone by the bend is going to be primarily in the midrange, as low frequency/long wavelength signals don't have a tendancy to reflect back. Here again those reflections will be removed via stuffing, and it's certainly an easy job to make sure of an adequte stuffing density by simply checking an impedance sweep for peaking.

[teodorom]

In order to better understand what I mean please take a look on the folllowing diagrams. They refer to a ML-TQWT, Scan-Speak 18W/4531G00, line lengh (calculated as stated): 173 cm.
The line is tuned at 33 Hz:

and around 100 Hz the SPL is flat:

If however frequencies around 100 Hz "see" a line only 10 % longer here is the result:

You can see that first resonace is a little bit lower.
Look then at the SPL graph:

the glitch at 100 Hz has become apparent.
Same situation if the line is 10 % shorter that the optimum:


The glitch at F7 seems unavoidable. Let's at least avoid the glitch at F3.
An please don't tell me that there is the stuffing to save the Queen !