Largely forgotten and overlooked independent research of exponential horns at Bell Labs, 1924.
The method of applying the theory of electrical networks to the horn, as used is due to P. B. Flanders and D. A. Quarles of the Bell Telephone Laboratories. The advantages of the method will be evident, if a comparison is made between the present text (1924!), and the treatment of the horn by A. G. Webster.
Horns have been extensively studied by P. B. Flanders, from whose most important memorandum the following quotation is taken, for the purpose of summarizing this article. The statement bears on the application of a horn to the short tube leading from the loud-speaking receiver diaphragm.
"Neglecting reflection effects, the addition of a horn does not effect an increase in the ultimate impedance at the end of a receiver opening. It does, however, cause that impedance to reach its ultimate value at a lower frequency; and the lower that frequency, the better, of course is the horn. The impedance "looking out" of a seven-tenths inch hole in an infinite wall reaches 80 per cent of its ultimate value at 9300 c.p.s.; a certain conical horn causes this 80 per cent value to be reached at 4200 c.p.s.; while the corresponding exponential horn causes this value to be reached at the relatively low frequency of 250 c.p.s. In a way these figures show why the exponential horn is so much superior to the conical type."
...The theoretical discrepancy is doubtless greater than that which would be observed in any practical case, because the wave front emerging from the large end of the horn can hardly be strictly plane; it is much more likely to be convex. And it may be noted that the smaller value for Y' as compared with Y at low frequencies happens to be more nearly in agreement with the smaller end correction for an unflanged tube (as compared with a flanged tube) which was noted by Rayleigh...
...There are many interesting problems in connection with horns, such as, for example, the directive effects in the radiation after it emerges from the mouth; the effects of dissipation; the effects of phase change, etc. It appears that some of the effects obtained with horns require considerable experimental study in order to elucidate them; unfortunately no discussion of these can be given, for lack of suitable data (which might have been available at Bell Labs, but was never published).
The method of applying the theory of electrical networks to the horn, as used is due to P. B. Flanders and D. A. Quarles of the Bell Telephone Laboratories. The advantages of the method will be evident, if a comparison is made between the present text (1924!), and the treatment of the horn by A. G. Webster.
Horns have been extensively studied by P. B. Flanders, from whose most important memorandum the following quotation is taken, for the purpose of summarizing this article. The statement bears on the application of a horn to the short tube leading from the loud-speaking receiver diaphragm.
"Neglecting reflection effects, the addition of a horn does not effect an increase in the ultimate impedance at the end of a receiver opening. It does, however, cause that impedance to reach its ultimate value at a lower frequency; and the lower that frequency, the better, of course is the horn. The impedance "looking out" of a seven-tenths inch hole in an infinite wall reaches 80 per cent of its ultimate value at 9300 c.p.s.; a certain conical horn causes this 80 per cent value to be reached at 4200 c.p.s.; while the corresponding exponential horn causes this value to be reached at the relatively low frequency of 250 c.p.s. In a way these figures show why the exponential horn is so much superior to the conical type."
...The theoretical discrepancy is doubtless greater than that which would be observed in any practical case, because the wave front emerging from the large end of the horn can hardly be strictly plane; it is much more likely to be convex. And it may be noted that the smaller value for Y' as compared with Y at low frequencies happens to be more nearly in agreement with the smaller end correction for an unflanged tube (as compared with a flanged tube) which was noted by Rayleigh...
...There are many interesting problems in connection with horns, such as, for example, the directive effects in the radiation after it emerges from the mouth; the effects of dissipation; the effects of phase change, etc. It appears that some of the effects obtained with horns require considerable experimental study in order to elucidate them; unfortunately no discussion of these can be given, for lack of suitable data (which might have been available at Bell Labs, but was never published).
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B. Kolbrek:
"It is perhaps less known that similar work on the theory of horns and horn loudspeakers was undertaken by the Western Electric Engineering Department, and patents by Henry C. Harrison in 1923 and Paul B. Flanders in 1924 show a clear understanding of the exponential horn and its mouth termination. The patents are good summaries of basic horn theory, and also show that it was known that the wave fronts in the horn are not plane but curved. A method to design a horn based on curved wave fronts with exponentially increasing area is described. It was Harrison who introduced the exponential horn to Western Electric, but the mathematical analysis was done by Flanders and Donald A. Quarles. The analysis by Flanders and Quarles was published as two internal memoranda in 1924, and it is clear that this material was not intended to be published: these memoranda are filed in an AT&T file case marked “strictly confidential”. Part of the theory (for the exponential horn only) was, however, published in the book “Theory of Vibrating Systems and Sound” by Irving B. Crandall in 1926. The analysis is interesting, in that it differs from the analysis of Rayleigh and Webster, and seems to have been derived independently of their work. Flanders’ memoranda also computed the response characteristics of a Western Electric horn speaker. These calculations used a lumped parameter model for the transducer and throat chamber, and the one-dimensional analytical solution for the horn. The mouth radiation impedance was that of a piston in an infinite baffle."
"It is perhaps less known that similar work on the theory of horns and horn loudspeakers was undertaken by the Western Electric Engineering Department, and patents by Henry C. Harrison in 1923 and Paul B. Flanders in 1924 show a clear understanding of the exponential horn and its mouth termination. The patents are good summaries of basic horn theory, and also show that it was known that the wave fronts in the horn are not plane but curved. A method to design a horn based on curved wave fronts with exponentially increasing area is described. It was Harrison who introduced the exponential horn to Western Electric, but the mathematical analysis was done by Flanders and Donald A. Quarles. The analysis by Flanders and Quarles was published as two internal memoranda in 1924, and it is clear that this material was not intended to be published: these memoranda are filed in an AT&T file case marked “strictly confidential”. Part of the theory (for the exponential horn only) was, however, published in the book “Theory of Vibrating Systems and Sound” by Irving B. Crandall in 1926. The analysis is interesting, in that it differs from the analysis of Rayleigh and Webster, and seems to have been derived independently of their work. Flanders’ memoranda also computed the response characteristics of a Western Electric horn speaker. These calculations used a lumped parameter model for the transducer and throat chamber, and the one-dimensional analytical solution for the horn. The mouth radiation impedance was that of a piston in an infinite baffle."
You bring up a good point... The bigger it is, the more directivity I'll get out of it, the link between SQ and directivity has been mentioned before. The issue has been the beaming but I think we've found a good compromise.
I'm not the expert but it has been suggested that it is the loading of any driver, with a horn, that causes an increase in efficiency which in turn lessens the amount of excursion required, which in turn decreases IMD. So before you worry about how you control what you are sending out, make sure sure the signal you are sending, is worth hearing. Even if only a 1-2db increase in efficiency, the reduction of excursion is significant enough to warrant an increase in sound quality, in particular, in the lower register of the driver. It might mean the difference between staying within or leaving xmax.
Directivity is somewhat negated by size, the wider the horn mouth, the larger range of frequencies it will direct. So there is no battle between the "loading" horn and the "directive" horn. People suggest that Salmon horns have no "Directivity Control" but thats a lie, it just doesn't "control" the directivity in a way that they find favorable, hence your confusion. A constant diretivity horn thats 15" a-round has the directive control over the same bandwidth as a Tractrix of the same diameter, generally speaking. What they do with the bandwidth within that range, is not the same.
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I agree. I'm constantly amazed with what Ro808 digs up. There is treasure in this thread.
He is illuminating the human technical way of thinking of yesterday to today, it is everthing that we have to talk about when people talk about a mature technology, old ideas should be still debated eternally IMO.
If you calculate the spl at max excursion at your planned listening distance, I think you will find that it exceeds what your ears could tolerate by far more than 1 to 2 db. Probably more like 10 db. A theoretical advantage is sometimes no advantage in practice.
Lets look at the disadvantages of using a horn larger than necessary.
1) larger center to center spacing will not be as kind to near field listening. This is especially relevant to you since you are intending to use them as monitors.
2) as Earl pointed out, you haven't given much attention to matching up the directivity of the horn to the directivity of the woofer. If you have an oversized horn, you polars will have a wrinkle at the crossover because you are crossing from a horn that is still directional to a woofer that is not.
Yes, maybe this thread needs a technical definition of what is meant with "loading"... I thought it meant a certain acoustic impedance greater than 1:1 (1:1 being any driver not facing any sort of horn or WG or cavity). For the frequency range that the particular impedance is maintained, the driver is said to be "loaded". Different horn/WG has different level of loading (efficiency).
Have to admit I maybe assumed it or made it up myself...
//
Have to admit I maybe assumed it or made it up myself...
//
Hi Camplo, my only experiences with larger horn are my recent synergy attempts.
The one I'm listening to now is a 60x40, with a mouth perimeter of 12.7 ft.
It's ability to make all the bass sound like it's coming from the horn far surpasses any of the smaller CD/horn and 12" cone designs I've built.
Oh, the synergy is crossing at 650Hz to the CD like all previous designs, so I think the integrated bass extension has to be due to horn size, not lower CD operation.
The thing also images better than any previous design too.
I've no idea whether to ascribe that to pattern control, or pulling the bass into the horn as just described, or simply the co-location of acoustic centers. I think I read someone say that synergies are made for high SPL and have too many issues to do well at lower volume. That is emphatically not my experience !
It's kinda funny, the synergy definitely measures a little weirder, than smoother horns like the xt1464.
But somehow, the acoustic co-location of the drivers on a larger horn easily overcomes whatever anomalies the straight sided horn walls, and holes in the horn make.
Anyway, larger horn? Go for it ! However you decide
Oh, one last comment...with whatever size horn you use, you might want to use the ka=2 guide, for matching cone directivities ...
I'm gonna use it if I decide to build another different size syn horn
The one I'm listening to now is a 60x40, with a mouth perimeter of 12.7 ft.
It's ability to make all the bass sound like it's coming from the horn far surpasses any of the smaller CD/horn and 12" cone designs I've built.
Oh, the synergy is crossing at 650Hz to the CD like all previous designs, so I think the integrated bass extension has to be due to horn size, not lower CD operation.
The thing also images better than any previous design too.
I've no idea whether to ascribe that to pattern control, or pulling the bass into the horn as just described, or simply the co-location of acoustic centers. I think I read someone say that synergies are made for high SPL and have too many issues to do well at lower volume. That is emphatically not my experience !
It's kinda funny, the synergy definitely measures a little weirder, than smoother horns like the xt1464.
But somehow, the acoustic co-location of the drivers on a larger horn easily overcomes whatever anomalies the straight sided horn walls, and holes in the horn make.
Anyway, larger horn? Go for it ! However you decide
Oh, one last comment...with whatever size horn you use, you might want to use the ka=2 guide, for matching cone directivities ...
I'm gonna use it if I decide to build another different size syn horn
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Yes, just trying to describe another less mentioned benefit of larger horns. (Oh, bass localization benefit not due to woofers in horn....synergy highpassed at 100Hz)
Agree btw, with your points about excursion, and difficulty with larger horns at matching directivity
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It's not seeing the reason, Rob - it's hearing the reason.
As I stated earlier, shallow waveguides can sound darn good at very low levels where the driver 'fram is hardly moving at all. Get beyond those levels and it sounds bad, you'll hear the driver in distress. Deeper horns can get much louder without that problem. Subjectively speaking you'll hear the music, not the speaker.
But why does it have to be an either/or? Can't we properly load the driver and have good directivity at the same time?
According to the Horn Doc.
Why do we want both?
Good loading:
- Reduces displacement
- Reduced displacement reduces IMD
- Resistance control (R > X ) improves transient response
Good directivity:
- 3D acoustic, cannot be equalized. It is what it is.
- Directivity determines spectrum of reverberant field vs direct sound
- Too little HF in reverberant sound: sounds dark
- Uneven reverberant sound: colored - even if on-axis response is flat!
Note:
The first and second argument in favour of good loading are the same thing, which makes good directvity (control) a clear winner.
However, this doesn't mean good loading is irrelevant.
Why do we want both?
Good loading:
- Reduces displacement
- Reduced displacement reduces IMD
- Resistance control (R > X ) improves transient response
Good directivity:
- 3D acoustic, cannot be equalized. It is what it is.
- Directivity determines spectrum of reverberant field vs direct sound
- Too little HF in reverberant sound: sounds dark
- Uneven reverberant sound: colored - even if on-axis response is flat!
Note:
The first and second argument in favour of good loading are the same thing, which makes good directvity (control) a clear winner.
However, this doesn't mean good loading is irrelevant.
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You already own the most obvious solution
Still, that solution qualifies for improvements.
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