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Old 18th December 2012, 11:53 PM   #101
xrk971 is offline xrk971  United States
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A picture of a 24 inch woofer cone
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Old 18th December 2012, 11:55 PM   #102
gpapag is offline gpapag  Greece
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These are a few things that I have to short out in my mind (where ? ) before i start build this kind of speaker design (cornu).
The 1st is the kind of loading that this construction provides to the driver's rear radiation.
The 2nd is how the speaker's placement (on the wall or away from it)affects this loading.
The 3rd is what happens with the "merging" of the acoustic output from the front of the driver and the rear output as it emerges from the side openings.

These three I consider to be within the "intended" modes of operation.
There are some more "unintended" ones which I should not touch now, namely, the acoustic output from the vibrating front (and rear)baffle which -detrimental or not- may be appreciable, the output due to diffraction at the edges and the effect due to acoustic "transparency" of the thin channel formers.

I am convinced that I should start from the intended 3rd , the merging of front and rear waves.
If they have the same phase they will add. If they are 180d out of phase they will cancel. In phase (+/- 45d max) is what I would like to achieve. How and at what frequency?

I guess I have to "choose" a driver first.
Size matters, here in favor of a very small driver (*).
A ~ 1" unit used almost invariably at computer speakers is a good choise.
Micro Speaker P/N YDT3434N-RB10F8 (W34.1*L34.1*H14.6) with concave membrane for multimedia,View loudspeaker,WBN Product Details from Shenzhen Wabony Electronic Co., Ltd. on Alibaba.com


Overall Size W34.1*L34.1*H14.6mm. Power Rated (Max.) 2.0 (3.0) W
Sound Pressure Level 82+/-3 dB @ 0.5m/1W
Characteristic Sensitivity 76 +/-3 dB Calculated value equivalent to 1m/1W
Resonant Frequency(fo) 250 Hz. Frequency Range fo~20000 Hz

I'll mount it on a large cardboard baffle (~1m x 1m) and do an impedance plot and a dirty FR sweep with the mic very close to the cone.
I'll keep the impedance plot for later comparison, noting for now the resonance frequency
The FR will show the LF roll off that I am interested for now.
Say it will start to roll off at ~600Hz and at 300 Hz is -12db.
Somewhere there, is the frequency -say at 400Hz- where and below, this unit will need the augmentation from the back loading. I keep this number: 400Hz shall be the crossover frequency. The upper end of the frequencies which the "horn" should provide for to help the driver to produce low frequencies.
Phase issue turns to path lengths issue. Front radiation path length and rear radiation path length.
So I have to pick a size for the rectangular construction to do the path length calculations

I have already turned to Dave's "cornu-clone spiral" pdf.
As it is in a scalable format, I have taken the length of five gray lines to represent a one scale unit (su). Thus, this su will depend on the size of the baffle. For a rectangular baffle of size X, one su represents a length of X/14

Baffle 200mmx200mm:---su=14.3mm
Baffle 300mmx300mm:---su=21.4mm
Baffle 400mmx400mm:---su=28.6mm
Baffle 500mmx500mm:---su=35.7mm
Baffle 600mmx600mm:---su=42.9mm
Baffle 700mmx700mm:---su=50.0mm
Baffle 800mmx800mm:---su=57.1mm
Baffle 900mmx900mm:---su=64.3mm
Baffle 1000mmx1000mm:-su=71.4mm

I will work for a while with su before turning into physical length units.

Based on Dave's drawing, the center of the speaker is 8 su from the center of each of the 4 mouths.

The horn spirals as drawn, represent two identical expanding pathways.
Each pathway starts from an opening (throat) on the rear chamber, expands for a distance and then splits into two expanding pathways of slightly unequal lengths (**), both ending at equal size openings (mouths).

The mean-path along each of the two main horn spirals is 40su (a better precision and analysis, later on).

So the sound from the rear has to run 40su distance till it will reach the edge, whereas the sound from the front has to run 8su distance. As they both run with the same speed (v~344m/s), the rear one will come delayed.

Doing an initial choice of the 200mm x 200mm baffle (su=14.3mm), I will have some real numbers of length and time

Rear sound needs (t=s/v)1.663ms to reach the end of the throat.
Front sound needs 0.333ms to reach the same throat end. The delay is 1.33ms

(I reach the same result as follows: I subtract the two path lengths. Rear 40su minus front 8su, equals 32su.
The 32su for this baffle is equal to 457.6 mm. Translated into time it is 1.33ms)

The "target" crossover frequency of 400Hz has a wavelength of 860mm and a period of 2.5ms

The time delay is close to half a period(or the equivalent path length is close to a half wavelength) of 400Hz.
This seems to be a complete cancelation case but it is actually the opposite, for the simple reason that the initiation point at the rear side of the driver is already 180d (or half a wavelength or half a period)out of phase with the front side of the driver.

So at the target freq waveforms add constructively.
What happens at the other frequencies?
At lower frequencies, due to increasing wavelengths, the existing time delay will not cause appreciable problems.
The problem will appear at higher frequencies. At a frequency which is double the frequency of the boost, there will be almost complete cancelation (in this scenario, the cancelation will occur at 750Hz).



(*) You will ask why such a small driver with such a high roll off freq.
Apart for the low price and avaliability, there are some technical reasons for such a choise for this experiment.
1. Measurements.
No big test baffle needed.
The room does not interfere at freq above ~200 Hz (no room modes).
2. Construction.
No large size prototypes needed.
Methodology is scalable and lessons learned (and calculations done) can be transferred to larger drivers/lower frequencies
The room (again)does not interfere at freq above ~200 Hz (no room modes). Results from speaker loading are away from room modes.
At higher crossover frequencies (say 400Hz), the ear discerns easily intensity variations and boosting by the horn. Not so at lower frequencies.

(**)Splitting of the pathway is considered a good practice as it allows bendings without back reflections in the flow of mid and high frequency acoustic waves.
Also, slightly unequal lengths allow some frequency spreading on the horn amplification).

Next time, study of the horn

George
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Last edited by gpapag; 18th December 2012 at 11:59 PM.
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Old 19th December 2012, 12:06 AM   #103
xrk971 is offline xrk971  United States
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Wow, awesome analysis George. I have much to learn. What I like about your analysis is that it allows us to follow reasoning and approach. Thank you.
Btw, I built a 14 in cornu with cheap 2 in driver (appears to resemble Visaton FRS5) and it sounds very nice. The plan layout is my own hand drawn based on cornu but nonetheless different - very round and channel spacings are different. I have path measurements (using strings laid on drawing) and can do similar analysis of how sounds combine by looking at propagation delay.
Regards,
Xrk971

Last edited by xrk971; 19th December 2012 at 12:10 AM.
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Old 19th December 2012, 12:50 AM   #104
Pano is offline Pano  United States
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Quote:
Originally Posted by xrk971 View Post
Pano,
When you made your spirals did you measure actual throat width in order to size depth?
I used the Planet10 PDF scaled to 20" and a depth of 2.5". Is that wrong?
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Old 19th December 2012, 01:10 AM   #105
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Originally Posted by Don Hills View Post
Even if the front panel is opaque, you could mount lights just inside the horn mouths aimed so as to provide "wall wash" light.
Exactly. Could be gorgeous. I did read your post about the art, and remembered seeing the website somewhere. Had to dig to find it. The lights would be a huge convincing factor.
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Old 19th December 2012, 01:35 AM   #106
xrk971 is offline xrk971  United States
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Quote:
Originally Posted by Pano View Post
I used the Planet10 PDF scaled to 20" and a depth of 2.5". Is that wrong?
What is your throat width from the drawing when printed to 20 inch size? I don't know if it is wrong ad you probably have throat smaller than Sd and that may actually give you better loading? I have always said to scale depth to match throat area with Sd, I had custom throat size and forgot to mention that.
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Old 19th December 2012, 01:37 AM   #107
xrk971 is offline xrk971  United States
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Can I do poor man's measurement by playing pink noise file and record then analyze spectrum of recorded sound?
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Old 19th December 2012, 03:15 AM   #108
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Default One disadvantage of foam core is ...

if you have something resembling a conventional box on the floor and an unknowing person tries to sit their big butt upon it and ... crush.

Good thing the cornu-copy-a is a wall-mount

If you must have it on the floor perhaps hot glue a bunch of pointy-end-up thumb tacks and other sharp objects atop it
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Old 19th December 2012, 04:22 AM   #109
xrk971 is offline xrk971  United States
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You can take a real pizza box and cover the cornu with it and hang on wall. Great speaker Decoration for a restaurant or a rec room type setting with pool tables big screen tv etc.
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Old 19th December 2012, 10:52 PM   #110
Pano is offline Pano  United States
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Originally Posted by xrk971 View Post
What is your throat width from the drawing when printed to 20 inch size?
I dunno. Can't measure until tomorrow evening. Will let you know before the world ends, if I can.

As for pink noise, yes, you could do that. You have to take into account the mic curve, but you can get a general idea. If you have a mic and a soundcard, use HOLMImpulse or ARTA for your measurement. Easy to get very good results.
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