Designing a dome faceted loudspeaker

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jeno
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Joined: Sun Jun 29, 2014 10:41 am

Re: Designing a dome faceted loudspeaker

Postby jeno » Sun Mar 17, 2019 5:59 pm

DeepSOIC wrote:
Sun Mar 17, 2019 4:33 pm
jeno wrote:
Sun Mar 17, 2019 3:41 pm
is the speaker on the picture a 5" Focal?
Nope. It's R2R Audio's one, made here in saint-petersburg, by a few guys in a small lab (almost a garage).
Interesting. Similar design idea like Focal. No dust cap and a fixed phase correction plug.
Remembers me on a long time ago. I also did some experiments with speakers and this an that, but there is a ugly ugly con .. the women acceptance factor :lol:
Anyway.. I hope I could help a bit. Maybe you change the dome a bit and use only 4 speakers. Could bring resonace frequency remarkably down.
Keep us updated

cheers
jeno
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DeepSOIC
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Location: Saint-Petersburg, Russia

Re: Designing a dome faceted loudspeaker

Postby DeepSOIC » Tue Mar 19, 2019 12:15 am

I think I am on to something.

I've opened a book "introduction to acoustics" by Rienstra and Hirschberg. There is a section for pulsating-sphere emitter. And man it's difficult to follow. Lots of math, with heavy reliance on symbols defined in earlier sections. And no pictures or practical examples to quickly relate to.
introduction to acoustics wrote:For a compact sphere the first term is dominating. We find exactly the result which we could anticipate from (2.59), the second derivative to time of the volume of the sphere is the source of sound. ... The second term of (6.9) is dominating for large sphere radii. In such a case the action of the wall movement is that of a piston which generates plane waves.
Nontheless, I think I managed to pick and decipher the two key pieces of math, for to derive frequency response of a sphere densely covered by point loudspeaker-like sources. (and after deriving it myself, and rereading the chapter, I realized the result was actually provided in the book, I just didn't recognize it).

For how I derived it, see attached .docx file. I just state here, that I got that for a sphere densely covered by small drivers with heavy cones, the frequency response of the sphere is not going to be flat, even if the drivers are small enough to be considered point-sources, and have ideal lack of directionality.

Specifically, the response is flat up to a corner frequency fc = c/(2*pi*R), where c is speed of sound and R is the radius of the sphere. (It is exactly when the circumference of the sphere equals one wavelength.) Below that frequency, the amplitude should fall like 1/f.

For my sphere, the corner frequency is about 1100 Hz. Go figure. So I multiplied the frequency response of the driver by this sphere-factor, and here's what I got:
theory testing.png
theory testing.png (93.63 KiB) Viewed 340 times
Apart from a small hiccup between 1.2-1.5k, the calculated response fits well with the measured one. From 2.8k, they deviate strongly, with real thing having much more output than expected. I would guess, this is because my drivers are too far apart, and above 2.8k they just stop collaborating to make that piston-like radiator, and behave more like a scattered set of point sources. Then probably going into beamy mode at circa 9k.

So I feel like I have a satisfactory explanation to that "BUT WHY" question.
Attachments
pulsating sphere frequency response (en).docx
(37.81 KiB) Downloaded 2 times
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DeepSOIC
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Location: Saint-Petersburg, Russia

Re: Designing a dome faceted loudspeaker

Postby DeepSOIC » Fri Mar 29, 2019 10:39 pm

This one has a surprisingly similar geometry to mine.
https://www.bksv.com/en/products/transd ... light-4292
OmniPowerSoundSource_Type4292 L_600x600.png
OmniPowerSoundSource_Type4292 L_600x600.png (404.43 KiB) Viewed 171 times