2" 223Hz tractrix horns

[mikebse2a3]

If you guy's want to debate this then you first need to decide what aspects of performance are important in a horn itself(good luck on this) and also what is the best compromise of performance options when combined with other sections of the loudspeaker system otherwise this could turn into pages and pages of debating in circles.

I think it would be good to go back to the basic and ask WHY HORNS...? What are the Real World benefits of a well designed Horn/Driver?

Frequency Response is just one part of a much more complex question about why a certain horn size might be the best compromise.

Then my next question is do or should you want a smooth well balanced on axis frequency response and off axis frequency response(ie: power response) from your horn and also your loudspeaker system as a whole?

What are the positive and negative of a system that maintains a smooth well balanced on and off axis response with controlled directivety?

What are the positive and negative of a system that doesn't provide a smooth well balanced on and off axis response with uncontrolled directivity?

The reason I pose the questions above is that in some way's horn size IMO will be determined by the above criteria and the need to combine the different loudspeaker sections(ie:LF, MF and HF). If you are combining for example a mid-range horn with a LF horn versus a direct radiator LF section or possibly a (large diaphram area like (4) - 15" drivers) direct radiator system .

mike tn[^o)]

[DrWho]

Another "expert" heard from!

Al K.

Wow, I'm flattered, but I really don't consider myself an expert.

[DrWho]

The reason I pose the questions above
is that in some way's horn size IMO will be determined by the above
criteria and the need to combine the different loudspeaker
sections(ie:LF, MF and HF)...

Thanks Mike, that was exactly my point. Performance goals in a competently designed system dictate the construction.

One
thing I will mention though is that a larger horn can always match the
behavior of a smaller horn, but a smaller horn can't always match the
behavior of a larger horn. That's why I say a horn can't be too big
when designed correctly.

[aj01]

Mike,

I've been reading a lot on horn theory and design to try and plan a diy project. One site I found said that for the high frequency cutoff of a horn - that the horn would start to beam at a wavelength 1/10th of the length of the horn. The other rules of thumb were that the cutoff of a tractrix horn should be ~2/3 the frequency of your crossover and a horn should only be designed to handle 3-4 octaves. Gothover's latest project looks like it is flat for over 4 octaves, so maybe this is too limitting.

Any comments on the above? Are there better references than what I'm finding on the web?

Thanks!

[Nat Denkin]

Mike,

I've been reading a lot on horn theory and design to try and plan a diy project. One site I found said that for the high frequency cutoff of a horn - that the horn would start to beam at a wavelength 1/10th of the length of the horn. The other rules of thumb were that the cutoff of a tractrix horn should be ~2/3 the frequency of your crossover and a horn should only be designed to handle 3-4 octaves. Gothover's latest project looks like it is flat for over 4 octaves, so maybe this is too limitting.

Any comments on the above? Are there better references than what I'm finding on the web?

Thanks!

According to Leo Beranek's book, Acoustics, eqn (9.33), the percent
2nd harmonic distortion for an infinite horn is given by
1.73(f/fc)*It^(.5)*10^(-2) where It is the power/square meter at the
throat. Thus, if a horn cut off is 200 Hz with an extreme slope crossover at that frequency, and we want the horn to
cover up to 3200 Hz for 4 octives, we have to consider how much distortion we would
accept. Assuming a 2" throat and a 1 watt acoustical 3200 Hz signal, that equates to It = 493 w/sq m so that the 2nd harmonic distortion would be about 6.1%. I recall that about 50% of music power is below 350 Hz and that the power drops off quickly above 1000 Hz. With "large" horn systems capable of handling over 100 watts (electrical), it would appear that distortion is a design factor.

Comparing a 2" diameter throat with a 1" diameter throat, we note (assuming both dimensions are exact) the smaller throat causes twice the distortion.

Thanks,

nat

[djk]

4x for a 0.7" throat (K55V) vs a 2" throat, or about 12dB difference.

In general, distortion is proportional to the square of the bandwidth in octaves. For a finite mouth the best solution is to cross the horn one octave above Fc, and run it about a decade (4.3 octaves above Fc). This would suggest horns with an Fc or 200hz and 2Khz being crossed at 400hz and 4Khz. By running a three-way we can select the mid driver for best performance rather than a fragile wide-band unit, and we can select a driver for a tweete based on its UHF performance, rather than on how well it can handle midrange.

[DrWho]

Mike,

I've been reading a lot on horn theory and design to try and plan a diy project. One site I found said that for the high frequency cutoff of a horn - that the horn would start to beam at a wavelength 1/10th of the length of the horn. The other rules of thumb were that the cutoff of a tractrix horn should be ~2/3 the frequency of your crossover and a horn should only be designed to handle 3-4 octaves. Gothover's latest project looks like it is flat for over 4 octaves, so maybe this is too limitting.

Any comments on the above? Are there better references than what I'm finding on the web?

Thanks!

Does that website provide physical principals that guide the recommendations, or is it more a case of observed correlation? And were the comments made in context of any specific flare rate?

I've found Olsen, Berenek, Post, and Keele to be pretty good resources for horn stuff. I know I've come across more authors too, but I'm real bad at remembering names.

[DrWho]

Assuming a 2" throat and a 1 watt acoustical 3200 Hz signal, that equates to It = 493 w/sq m so that the 2nd harmonic distortion would be about 6.1%.

I just wanted to mention that 1 acoustic watt on a horn with a DI of 10dB is going to be over 117dB SPL at 1m in full space. You could see as much as 125dB SPL at 1m in a true 1/8 space environment. Cut the power back 20dB (100x less power) and you're looking at 0.061% 2nd harmonic distortion from 105dB SPL at 1m in 1/8 space.

I believe Beranek's comments are also assuming that the driver is adding no distortion...yet we know that the driver tends to dominate the distortion signature (in a good horn). There's the distortion introduced by the phase plug too.

Did Beranek specify the type of horn when deriving that formula? I'm guessing it's for an exponential horn, but I could be mistaken. I would expect the distortion to be less for a conical horn than for an exponential horn.

[aj01]

This was the specific web-site that I was refering to: (mainly refers to Bruce Edgar or other pages that are from him or Voights)

http://www.rocketsciencecanada.com/rocketsciencecanada/Sound/Horns/Info_SizeShape.asp

http://www.rocketsciencecanada.com/rocketsciencecanada/Sound/Horns/Info_Design.asp

Hmmm, I can't find the 1/10th of a wavelength comment right now. I'll have to look through some bookmarked pages to find that. I thought that the 1/10th number was based on dispersion rather than distortion though... This is from memory and a couple of months ago, so I could be wrong.

Thanks for the author names. I'll have to do some researching and buy a couple of books.

[Nat Denkin]

Assuming a 2" throat and a 1 watt acoustical 3200 Hz signal, that equates to It = 493 w/sq m so that the 2nd harmonic distortion would be about 6.1%.

I just wanted to mention that 1 acoustic watt on a horn with a DI of 10dB is going to be over 117dB SPL at 1m in full space. You could see as much as 125dB SPL at 1m in a true 1/8 space environment. Cut the power back 20dB (100x less power) and you're looking at 0.061% 2nd harmonic distortion from 105dB SPL at 1m in 1/8 space.

I believe Beranek's comments are also assuming that the driver is adding no distortion...yet we know that the driver tends to dominate the distortion signature (in a good horn). There's the distortion introduced by the phase plug too.

Did Beranek specify the type of horn when deriving that formula? I'm guessing it's for an exponential horn, but I could be mistaken. I would expect the distortion to be less for a conical horn than for an exponential horn.

Yes, it was for an "infinite" exponential. He notes that most of the distortion would occur near the throat. Any horn that expands more rapidly should have less distortion from this source.

IM distortion would probably be more annoying than harmonic, anyone have a handle on that?

Thanks,

nat

[Al Klappenberger]

Dennis,

"In general, distortion is proportional to the square of the bandwidth in octaves."

I have heard this before but never understood it. My main question is bandwidth of what? I would think bandwidth would be set my the crossover frequency which the horn would know noting about. Is it simply now far up in frequency the horn is asked to propagate energy relative to its low end Fc? That is, the bandwidth of spectrum that is fed to it? That would make sense.

Al K.

[djk]

It has to do with the cut-off frequecy of the horn. The lower the cut-off frequency, the slower the expansion rate, and the more the higher frequencies become distorted. Because of this it's the ratio of the cut-off frequency to HF that matters, not the lower crossover point you choose (ie: a 500hz crossover with a 200hz horn, think Altec 311-90). One design practice is to use a rapid initial expansion, this makes the horn shorter, and also reduces HF distortion.

[Al Klappenberger]

Dennis,

I would like to compare a few tractrix horns expansion to see if I can see that trend, that is, the slower expansion rate with a lower cutoff. I assume I can compare the ratio between the areas between two chosen points near the driver to see that difference, say, between 1 in and 2 inches from the driver in several horns, all designed using the Tractrix equation. It's logical to visualize a longer horn having a slower expansion rate, but I want to see how other parameters change at the same time. That is, mouth size, driver size, length, Fc and whatever else comes up.

Also, is this type distortion related to throat pressure? Do shorter wavelengths inherently have higher pressure?

AL K.

[DrWho]

I recall Tom Danley mentioning something along the lines that distortion is generated because the wave velocity changes as a
function of density of the medium - so the modulating air pressure
creates a modulated wave velocity which shows up as distortion. It
matters more at higher frequencies because the wavelengths are shorter
- thus a fixed velocity modulation has a larger relative impact on the
waveform. The more constricted the throat, the greater the air pressure.

Danley could have been referring to behaviors that happen at much higher SPLs though...I'll have to find his comments again to know for sure, but I think it makes sense conceptually.

[Al Klappenberger]

Dennis,

" It has to do with the cut-off frequency of the horn. The lower the cut-off frequency, the slower the expansion rate"

It dawned on me after I went to bed that these factors are directly related anyhow.

In the tractrix horn design program I wrote I included (In "C"):

fc = log(area / a1) * 1050.42 / (x1-c);

"x1-c" is the distance between the two areas "area" and "a1"

So I don't have to crunch any numbers at all. There it is! Larger mouth, longer horn. lower cutoff and more high frequency distortion!

Daaahhh... NEAT!

Al K.

[ClaudeJ1]

Dennis,

" It has to do with the cut-off frequency of the horn. The lower the cut-off frequency, the slower the expansion rate"

It dawned on me after I went to bed that these factors are directly related anyhow.

In the tractrix horn design program I wrote I included (In "C"):

fc = log(area / a1) * 1050.42 / (x1-c);

"x1-c" is the distance between the two areas "area" and "a1"

So I don't have to crunch any numbers at all. There it is! Larger mouth, longer horn. lower cutoff and more high frequency distortion!

Daaahhh... NEAT!

Al K.

So does this lend even greater credibility to Earl Geddes "High Orde Modes" science in horns vs. his Oblate Spheroid Waveguides?

[djk]

HOM is code for internal reflections in the horn.

The lowest reflections are from a axis-symetrical (round) horn that has the same taper rate from inside the driver all the way to the mouth.

The popular TAD monitors designed by Keith Holland were a double 15", 10", and a round horn designed for the 1" TAD 2001.

'Around the Horn' by Keith Holland was published in Speaker Builder 8/94.

http://www.audioheritage.org/vbulletin/showthread.php?t=12967

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Posted by djk (M) on November 27, 2004 at 00:23:28
In Reply to: Re:
Soundstage depth and horns... posted by GedLee LLC on November 26, 2004
at 15:25:16:


This is mainly for Paul and eso:
Dr
Keith Holland BSc PhD did his thesis on horn loudspeakers at the
Institute of Sound and Vibration Research (ISVR), University of
Southampton.

Excerpts were published in Speaker Builder
Magazine (Reflecting on Echoes and the Cepstrum, 1996) and Liberty
Instruments offered some dedicated test equipment.

Echos were
found in many horns.

A new horn was designed to have no
echos.

It was found that any change in the taper rate of the
horn/driver combo, any inside corner, or diffration slot, produced
reflections inside the horn (echos).

The new horn was
circular and had the same taper rate as the stub inside the driver.


The new horn was based on the TAD2000 series driver and was
crossed at the point where it had the same directivity as the mid-bass
driver.

After the success of the Holland monitor, Yamaha and
Ramsa both came out with a series of products based on these ideas.


JAES:

Volume 38 Number 3 pp. 148, 149; March 1990
(Comments on "Impulse Measurement of Acoustic Impedance")


Volume 44 Number 1/2 pp. 23-36; January/February 1996 (The Sound of
Midrange Horns for Studio Monitors)

Volume 44 Number 7/8 pp.
569-580; July/August 1996 (A Model of Nonlinear Wave Propagation in
Horns)

"It is concluded that the reflections from the mouth
termination of long horns is responsible for the characteristic sound
and that for studio monitor applications, a midrange horn should have a
length not exceeding 340 mm and should be free of flare
discontinuities."

"A blind listening test is described in
which 16 loudspeakers are compared with four reference loudspeakers
under anechoic conditions. The test is concerned with the perceived
sonic similarity between midrange horn loudspeakers and direct radiators
and is intended to pinpoint the physical cause of a "characteristic
sound" attributed to many studio monitor systems equipped with
midfrequency-range horns. Comparisons are made between the listening
test results and measurements of on-axis frequency response. The results
indicate that short horns sound more similar to direct-radiating
loudspeakers than long horns."

[Al Klappenberger]

Would "any inside corner" refer to the square cross section of the Edgar type wood horns that everyone (including me) is making lately? I wouldn't think that wouldn't be a problem considering that microwave RF transmission lines, that is waveguides, are usually rectangular in cross section. They propagate energy nicely without reflections. The acoustic wavelengths at high audio frequency are a fraction of an inch and so are the electromagnetic wavelengths at microwave RF. Microwave waveguides and horn throats are also around the same size. From what I have seen, similarities like this usually illustrate similar characteristics. I ask because I have a fair grasp of TEM mode stuff in coaxial lines, but I never really understood waveguides. They are used at frequencies that are well above the world of L-C filters so I never bother to look into them. If there is a direct correlation between horns and microwave waveguides, I need to do it.

Al K.

[John Warren]

A square wave is the harmonic sum of sine waves.

Want to reproduce a 500Hz square wave with no distortion? You need bandwidth.

F(t) = sin(F) + 1/3 sin(3F) + 1/5 sin(5F) + 1/7sin(7F) + 1/9 sin(9F) + ...to infinity

If the system cannot reproduce a 4500Hz sine wave (=9F), the 500Hz square wave will be distorted.

Bandwidth, transient response and distortion are related, debit bandwidth and debit transient response and increase distortion.

Blame Fourier.

[Al Klappenberger]

And to think I was worried that what I was saying might not be relevant to the discussion!

Al K