Gradient 1.4 inspired: Question from Linkwitz Lab page (U-H woofer) - is it related to speed of sound in damping materials?

Hi,

I want to build Gradient 1.4 inspired speaker: something with downfiring woofer and coax with cardiod behavior.
Was looking at that beautiful stockpile of acoustic resources at Linkwitz Lab and stumbled on this:

Upolar1mod.gif


Gradient 1.4 (I think) is cardioid or cardioidish in mid-high frequencies because it uses exactly the same principle described here: some resistive material which partially restricts sound from the back by absorbing it.
I want to replicate it to get cardioid-like behavior.

Here is quote from
https://www.linkwitzlab.com/H-U woofer2.htm
Cpract1.gif


Rather than using an electrical delay T it is possible to derive the necessary delay from lumped acoustic elements as sketched in (B). The compliance of the air volume inside the box corresponds to an acoustic capacitor. In combination with the flow resistor ZF it forms an RC lowpass filter. Below its cut-off frequency the lowpass has nearly constant delay. The difficulty in this approach lies in finding a practical flow resistor of the necessary value, linearity and flat frequency response. It is difficult to obtain a resistor that can handle the large volume flows required for a woofer and (A) becomes the best solution. For higher frequencies variations of the concept in (B) can lead to cardioids with very wide bandwidth. By proper dimensioning of various parameters the roll-off of the rear radiation, due to the lowpass filter, can be made to coincide with the decrease in rearward radiation from the front side of the box, due to front baffle size and driver diameter becoming acoustically large. When combined with a coaxial tweeter, that takes advantage of the horn like nature of the midrange cone, it becomes possible to extend the unidirectional frequency range even further. A commercial example is the Revolution loudspeaker by Gradient Ltd. .

The question is how that absorbtion works:
Does the the speed of sound get reduced inside flow resistor and this is causing some delay to back wave?
or
It just reduces the pressure of sound (SPL), speed stays the same and because of that we get asymmetric dipole with cardioid-ish behavior?
From Linkwitz Lab page I am 99% sure that this has to be velocity related, because we need some kind of preferably uniform delay in wide frequency range for it to work, so the speed of sound has to be less in that mechanical flow resistor to get that delay. Right?

Lets assume I want mechanical cardioid for the coax part of the speaker, with as little of no dipole behavior. Then the question is - from which practical material to make flow resistor and how to calculate the right amount, thickness, approx fiber length, density, etc at least to the level to start practical experimentation? Are there those calculations available at all or all I need is to buy some Rockwool and start experimenting? Is there some science to it?

Can someone help me with this?
Than you.
 
Story https://www.inner-magazines.com/audiophilia/defending-the-objective-approach/

Test with measurements
https://www.lowbeats.de/test-gradient-1-4-ungewoehnliche-koax-standbox-im-kegel-design/

My clone thread. I paid no specific attention to low mid radiation. Just the opening on the backside and loose polyfill. Notice that the motor structure of the coaxial driver fills more than half of the ball! Cardioid operation always works only at narrow freq area, typically one octave (e.g. 500-1000Hz)
https://www.diyaudio.com/community/threads/seas-mr18-3-way.322839/
 
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My clone thread. I paid no specific attention to low mid radiation. Just the opening on the backside and loose polyfill. Notice that the motor structure of the coaxial driver fills more than half of the ball! Cardioid operation always works only at narrow freq area, typically one octave (e.g. 500-1000Hz)
https://www.diyaudio.com/community/threads/seas-mr18-3-way.322839/
Juhazi,
Nice documention on your build, but... There are many differences to what I want to build: passive and... cardioid. Is your speaker top "sphere" cardioid with holes in the back, or is it closed?

And where you found information that cardioid works only at narrow freq? I definitely want to read more about this
 
Hi, passive is a real challenge, but of course doable.

Cardioid being narrow range applies to this kind of resonance-based systems like in Linkwitz example you showed. Sensitivity drops fast with low freq, it will need lots of eq and driver excursion, distortion gets high easily. Midrange is easier and it nicely matches with waveguide tweeters (or coaxial tweeters)

D&D 8c is a case to study! https://www.erinsaudiocorner.com/loudspeakers/dutch_dutch_8c/ Even it has highish distortion at 200Hz

1710789336680.png


1710790376216.png


https://www.diyaudio.com/community/...id-active-speaker-insipired-by-d-d-8c.369939/

Gradient 1.4 doesn't even try to be cardioid as low as D&D. WM xo is 200Hz https://gradient.fi/index.php?id_product=9&rewrite=gradient-14&controller=product&id_lang=1

I haven't found directivity measurement of 1.4
 
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Hi, passive is a real challenge, but of course doable.

Yes... Thats why community here is strong - we do projects which at the begining looks like Moonshot
Cardioid being narrow range applies to this kind of resonance-based systems like in Linkwitz example you showed. Sensitivity drops fast with low freq, it will need lots of eq and driver excursion, distortion gets high easily. Midrange is easier and it nicely matches with waveguide tweeters (or coaxial tweeters)

Ok... Lets assume I am setting some reasonable goal to make cardioid-ish behavior in frequency from subwoofer or some downfiring woofer (or front facing woofer) upper range until tweeter in waveguide - that is from~200 to 2500-3000Hz. Is this range reasonable or should I make lesser goal?


Directivity of this speaker is exactly the reason I want to build my project. Budget is not as big to go with active system, so have to stick to smth simpler. My inner voice of reason says that the speaker with good directivity will save lots of tuning and eq-ing headaches. The THD in the graph is indeed high in 60-200Hz range for speakers costing 10k+ EUR but THD is less important than good IMD and directivity values.
https://www.diyaudio.com/community/...id-active-speaker-insipired-by-d-d-8c.369939/
Gradient 1.4 doesn't even try to be cardioid as low as D&D. WM xo is 200Hz https://gradient.fi/index.php?id_product=9&rewrite=gradient-14&controller=product&id_lang=1

I haven't found directivity measurement of 1.4

I haven't found 1.4 directivity data too. From memory I am almost sure I saw some 360 deg pattern of this speaker, not sure if hand painted or graph of measurement, where it was smth between dipole and cardioid in mid range.

Idea passed my mind that if we put in the back of the speaker driver the sound speed reducing material which also absorbs some sound SPL - we can get passive cardioid. The question is if there is such material suitable to get more or less uniform results from ~200Hz to ~2500Hz
 
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