Re: back to cardioid
A decent paper, but I'd be careful drawing any conclusions from it. Only there source points were used, and only one listener point, hardly a survey of the possibilities. And one source point is notably bad for the monpole and no one would ever put a sub there (center of the room). Clearly the author has a bias for cardiod and picks the data to best fit his preference. I could easlily write a counter paper with three points that showed a better monopole.
When I did my study in 2000 I had no preference. I was working at Ford at the time and we wanted to know which kind of sub worked best.
Only later did I start to make subs and I made them based on what I learned when I had no preference.
I have serious reservations regarding the objectivity of a paper done by someone who has already decided the answer.
Etienne88 said:
A decent paper, but I'd be careful drawing any conclusions from it. Only there source points were used, and only one listener point, hardly a survey of the possibilities. And one source point is notably bad for the monpole and no one would ever put a sub there (center of the room). Clearly the author has a bias for cardiod and picks the data to best fit his preference. I could easlily write a counter paper with three points that showed a better monopole.
When I did my study in 2000 I had no preference. I was working at Ford at the time and we wanted to know which kind of sub worked best.
Only later did I start to make subs and I made them based on what I learned when I had no preference.
I have serious reservations regarding the objectivity of a paper done by someone who has already decided the answer.
Re: Re: back to cardioid
I am afraid that conclusions are easily drawn in many cases and become widespread ideas. Especially in audio, which evolved to be very much of an ambiguity zone.
The following comes from Wikipedia
''Dipole loudspeakers, such as electrostatics or ribbons, couple to the room differently, by velocity rather than pressure, and are generally thought to excite resonant peaks less.''
gedlee said:
I am afraid that conclusions are easily drawn in many cases and become widespread ideas. Especially in audio, which evolved to be very much of an ambiguity zone.
The following comes from Wikipedia
''Dipole loudspeakers, such as electrostatics or ribbons, couple to the room differently, by velocity rather than pressure, and are generally thought to excite resonant peaks less.''
Re: Re: back to cardioid
Um, Ok... But why should we assume that the author had already decided the answer? Is that in the paper somewhere that I missed?
Could it be that Mr. Ferekidis did the research first, then wrote about what he found to be best?
What bothers me is the he carefully makes his case for 9 pages and then throws in figure 15 which seems to show that the dipole is just as good as the cardioid in the same position. If the position had been chosen to favor the monopole, how would the other 2 fare?
gedlee said:
Um, Ok... But why should we assume that the author had already decided the answer? Is that in the paper somewhere that I missed?
Could it be that Mr. Ferekidis did the research first, then wrote about what he found to be best?
What bothers me is the he carefully makes his case for 9 pages and then throws in figure 15 which seems to show that the dipole is just as good as the cardioid in the same position. If the position had been chosen to favor the monopole, how would the other 2 fare?
Re: Re: Re: back to cardioid
It seemed from the photos that he had a well developed speaker - not a prototype at all, which is what a researcher would have done. No researcher would have made a final product not knowing what product to build. Am I right?
He would have had to made three prototypes, do the tests, then design and make a pair of finished products and finally write the paper with the photos. Just doesn't seem like what was done, but I suppose it could happen. And why not show all of the test samples?
panomaniac said:
It seemed from the photos that he had a well developed speaker - not a prototype at all, which is what a researcher would have done. No researcher would have made a final product not knowing what product to build. Am I right?
He would have had to made three prototypes, do the tests, then design and make a pair of finished products and finally write the paper with the photos. Just doesn't seem like what was done, but I suppose it could happen. And why not show all of the test samples?
I'm glad the paper is getting some interest!
About figure 15: yes, on this figure, dipole is as good as cardioid. But then if you look at figure 9 (speaker in the corner), monopole is as good as cardioid. My point is you can get it "right" with any type of bass speaker if you put the speaker at the "right" position. According to Ferekidis study the cardioid is less sensible to positioning, which is new to me. And which seems pretty good when it comes to negotiating the positioning of your 2, 3 or maybe 4 subwoofers with your partner!
My personal reservation about dipoles is the fact that they excite the room modes best when placed in the pressure nodes (where the pressure is low). The pressure nodes does not coincide in any place in the room, thus you will never get a dipole exciting all the modes of any given room.
Monopoles excite the room modes best when placed in a high pressure zone. The corners of a room are high pressure zones. You thus have 4 positions to place your monopole subs.
Those of you who are interested in room acoustic and loudspaeaker/subwoofer placement can have a look at the following paper. Examples are given for a 2 subwoofers set up.
I understand that Earl does not like very much this paper. Earl preaches for multiple monopoles and the paper shows that cardioids are better since less sensible to positioning. I fully agree with Earl that they only used one source point and used quite extreme positioning. But to me, it was done in order to emphasis their points. For example the mic was placed in the corner (which is the least plausible listening position!) in order to pick up all the excited modes of the room. They should have nevertheless extend their study to 2 points source and maybe more. The paper seems well written to me (from a scientific point of view) and I would be happy to discuss its validity but only if it is scientific argumentation...
Monopoles certainly have their advantages: they can pressurize the room below its lowest mode which neither dipoles nor cardioids can. Monopoles don't have the 6dB roll off at low frequencies which puts high requirements on excursion when it comes to dipole/cardioid.
So, as you see, it is not all black or all white... it always comes back to compromises and which ones your are ready to make!
If you excite a room mode, it will resonate and have a certain decay time. This is not speaker type dependent, it is room dependent! As Earl said earlier, the room dominates the situation here... So a key to good bass response is room treatment. I'm thinking here about bass traps and/or tuned Helmholtz resonator to shorten as much as possible these nasty resonant tails. (Absorption could work as well but seems to be less efficient) This kind of room treatment is generally pretty bulky so that many prefer to live without it... I would call that making the wrong compromise! I unfortunately don't have any hard facts about it, it comes from my readings in the Master Handbook of Acoustics, so please be nice with me!
Regards,
Etienne
About figure 15: yes, on this figure, dipole is as good as cardioid. But then if you look at figure 9 (speaker in the corner), monopole is as good as cardioid. My point is you can get it "right" with any type of bass speaker if you put the speaker at the "right" position. According to Ferekidis study the cardioid is less sensible to positioning, which is new to me. And which seems pretty good when it comes to negotiating the positioning of your 2, 3 or maybe 4 subwoofers with your partner!
My personal reservation about dipoles is the fact that they excite the room modes best when placed in the pressure nodes (where the pressure is low). The pressure nodes does not coincide in any place in the room, thus you will never get a dipole exciting all the modes of any given room.
Monopoles excite the room modes best when placed in a high pressure zone. The corners of a room are high pressure zones. You thus have 4 positions to place your monopole subs.
Those of you who are interested in room acoustic and loudspaeaker/subwoofer placement can have a look at the following paper. Examples are given for a 2 subwoofers set up.
I understand that Earl does not like very much this paper. Earl preaches for multiple monopoles and the paper shows that cardioids are better since less sensible to positioning. I fully agree with Earl that they only used one source point and used quite extreme positioning. But to me, it was done in order to emphasis their points. For example the mic was placed in the corner (which is the least plausible listening position!) in order to pick up all the excited modes of the room. They should have nevertheless extend their study to 2 points source and maybe more. The paper seems well written to me (from a scientific point of view) and I would be happy to discuss its validity but only if it is scientific argumentation...
Monopoles certainly have their advantages: they can pressurize the room below its lowest mode which neither dipoles nor cardioids can. Monopoles don't have the 6dB roll off at low frequencies which puts high requirements on excursion when it comes to dipole/cardioid.
So, as you see, it is not all black or all white... it always comes back to compromises and which ones your are ready to make!
If you excite a room mode, it will resonate and have a certain decay time. This is not speaker type dependent, it is room dependent! As Earl said earlier, the room dominates the situation here... So a key to good bass response is room treatment. I'm thinking here about bass traps and/or tuned Helmholtz resonator to shorten as much as possible these nasty resonant tails. (Absorption could work as well but seems to be less efficient) This kind of room treatment is generally pretty bulky so that many prefer to live without it... I would call that making the wrong compromise! I unfortunately don't have any hard facts about it, it comes from my readings in the Master Handbook of Acoustics, so please be nice with me!
Regards,
Etienne
Etienne88 said:
I don't know when the paper was written, but the conclusions are effectively the same as those of Backman (2003).
That is incorrect. Cardioids are able to pressurize a room. Cardioids have finite volume displacement over a cycle. This should be obvious form the decomposition of a cardioid response to that of a monopole + that of a correctly equalized dipole. The dipole part contributes nothing to the net volume displacement while the monopole part obviously remains the same as a monopole alone. This is one of the advantages of a dcardioid over a dipole., assuming room pressurization is considered an advantage.
Hi John,
When it comes to cardioid speakers, two ways are presented in the paper from Ferekidis (one more is presented at the beginning of this thread): the first one is a monopole with a dipole on top of it, the second one is a semi open back construction.
I understand that the first one will be able to pressurised the room below its lowest resonant frequency. But will the semi open back be able to do that as well? I have the feeling that it will but to a lower extend...
Regards,
Etienne
Thank you for putting me back on the right track!
When it comes to cardioid speakers, two ways are presented in the paper from Ferekidis (one more is presented at the beginning of this thread): the first one is a monopole with a dipole on top of it, the second one is a semi open back construction.
I understand that the first one will be able to pressurised the room below its lowest resonant frequency. But will the semi open back be able to do that as well? I have the feeling that it will but to a lower extend...
Regards,
Etienne
Etienne88 said:
Good question, though somewhat academic. In theory it should but in practice it probably isn't as much as an issue as the required cones excursion. Be it a dipole/monopole combination, an acoustic resistance box, or a true cardioid (two monopoles with separation, inverted phase and an added delay to one) the ability to pressurize will be limited by excursion. With a sealed box monopole the woofer Fs leads to constant excursion below Fs and correctly coupled to a room the pressurization effect balance the natural woofer roll off. But with any cardioid, to maintain the same behavior would require excursion increasing at 6dB/octave as the frequency drops, al the way to DC, and excursion limits are exceeded quickly for any reasonable SPL. So the eq is curtailed based on the design requirements to obtain a target SPL at a target woofer Fs and below that the room pressurization will only increase at 6dB/octave, assuming no additional roll off of the eq.
In a unbiased paper you don't pick the point that support your hypothesis - thats call bias - which is what I was critical of.
By the way I do strongly recommend the Toole paper that you posted and then my book (being posted for free at my web site) because I show practicle was to impliment what Floyd and I both agree needs to be done.
Certainly more IMO. The only way to discuss this "which source is better" discussion is with good statistics because one can always poick situations which benefit one type over the other. Floyd does this and I do it too, but the subject paper did not. This takes away a lot of credibility.
John first appears to complain that this isn't true and then seems to state that it is. I'm not criticizing John, but I found his discussion contradictory (maybe I misunderstood). I agree to his first claim that a cardiod can pressurize a sealed room, just as a monopole, but not at the same rate as a monopole for a given cone excursion. I think that this was his second point, although I found that somewhat confusing.
Once again, the issue to me is about how to best utilize a given number of drivers and physical sizes for the best LF sound field. Dipoles can't do the job because they NEED a monopole at the very lowest frequencies. A cardiod could, but I would prefer to use two drivers as two independent monopoles (in bandpas enclosures) for a smoother response. Now if you make a cardiod out of a single driver then there is no way that it isn't a dipole at the very LF and you are right back to the need for a monopole.
Constraining the problem with two drivers, and a limited amount of amp power (voltage level) I would bet on the use of two monpoles (bandpass prefered) as the best solution (smoothest response with highest level) every time in any room. Different constraints may lead to different conclusions, but these constraints seem reasonable to me.
John, did you ever read my purely passive cardiod enclourse design using an Acoustic Level? I always wanted to build one, but never did.
Earl, I am more than happy that you strongly recommends some readings about room acoustics. I have the feeling that it is the weakest link in too many hifi installation... it is like a taboo topic and I don't understand why? I was once living in a flat where the living room was 5 meters by 5 by 2,5. I never succeed in getting my system right despite bass traps, absorbing panels and following Toole guidelines. I was about building tuned resonators but then we moved...
Bottom of the line: room acoustic has to be taken seriously!
I did get the point about credibility. I hope I was not too critical about your critics!
I found a link for the German paper I was referring to (about improved control of room mode excitation using multiple low frequency cardioids in multi-channel systems), it is in English this time! here
They found out that the decay time is lower for multiple cardioids than a single monopole... which did not convinced me! since I believe that the decay time is room dependent, not speaker dependent. So I would be happy to hear your opinion about it!
By the way I hope that the time axle on the decay graphs is in ms, not seconds as printed!
Regards,
Etienne
Bottom of the line: room acoustic has to be taken seriously!
I did get the point about credibility. I hope I was not too critical about your critics!
I found a link for the German paper I was referring to (about improved control of room mode excitation using multiple low frequency cardioids in multi-channel systems), it is in English this time! here
They found out that the decay time is lower for multiple cardioids than a single monopole... which did not convinced me! since I believe that the decay time is room dependent, not speaker dependent. So I would be happy to hear your opinion about it!
By the way I hope that the time axle on the decay graphs is in ms, not seconds as printed!
Regards,
Etienne
Etienne88 said:
Nobody wants to deal with the room problem. The WAF is even higher when you want to change the room. Its also a lot more complex than just buying speakers and cables.
This paper is better, but I still get the impression that they are trying to prove that cardiods work best, not WHICH works best. I'd like the chance to read it more thoroughly before commenting much more, but some of there conclusions seem unfounded by the data. They do agree with me that the more subs the better, they just seem to believe that cardiods do a better job than monopoles and I don't see where they did enough testing to prove that point. It seems that they jumped to it based on a very few comparitive tests of the three source types - which all had the same LF response??I found a link for the German paper I was referring to (about improved control of room mode excitation using multiple low frequency cardioids in multi-channel systems), it is in English this time! here
They found out that the decay time is lower for multiple cardioids than a single monopole... which did not convinced me! since I believe that the decay time is room dependent, not speaker dependent. So I would be happy to hear your opinion about it!
By the way I hope that the time axle on the decay graphs is in ms, not seconds as printed!
Regards,
Etienne
And I agree with you that there is no obviuos reason why the mode damping would be source dependent. I mean in theory it certainly is not.
I'd still stay with my bet that four drivers in a monpole configuration would work better that the two cardiods that you could make with these same four drivers.
I think that is simple to conclude, that in the nether regions, is not clever to lose energy. But to distribute energy. So distributed monopoles is automatically the clever solution. The whole discussion boils down to mind frames of people who have done reinforcement and pro installations VS only High-End or Studio. The first bunch seeks practical efficiency, the second bunch seeks Avalon.
gedlee said:
Maybe I was a little too quick and to complicated. There is nothing puzzling about it. Let me pose it in another way. Given the same free field acoustic response the cardioid will pressurize a room the same as a monopole. But if the free field acoustic response has less than a 3rd order roll off below the woofer system’s Fc, the excursion of the cardioid (or dipole component there of it, if a compound cardioid (MP + Eq'ed DP)) must continue to increase to infinity at DC which is physically impossible. On the other hand, if the free field response has a 3rd order roll off then the cardioid (or DP component there of) would only need to maintain constant excursion below the woofer's Fc, in which case it would be possible. If the roll off is higher than 3rd order then the excursion will decrease. The required excursion of the cardidid (or DP componet) required to match the monopole goes like order (3-n) where n is the order of the free field roll off. Maybe that is a little clearer.
Why do you say that? If a cardioid is made from two drivers separated by a distance, d, with an additional (electronic or digital) delay of d/c applied to the rear driver then the on axis phase difference is 180 + w(2d/c), at 90 degree off axis it is 180 + w(d/c) and from the rear is 180 and not a function of w.
Now if you make the cardioid with a single driver in an acoustic resistance box the electronic delay is replaced by the delay of an acoustic low pass fitter tuned to yield a the same delay as w goes to zero. The same phase relations exist on axis, at 90 degrees and from the rear. It is true that at w=0 (DC) the phase difference goes to zero at all off axis angles, which is also true for a dipole, but that doesn't make a cardioid a dipole at low frequency. What it does say is that the outputs of an unequalized cardioid and an unequalized dipole (both 1st order gradient sources) tend to zero at DC is approached. That doesn't mean that the radiation pattern of a cardioid becomes a dipole as DC is approached. At any frequency greater than zero the on axis, 90 degree and from the rear phase relations remain. What happens at DC is really rather academic because even for a monopole, to have flat free field response to DC would require infinite excursion. At any practical low frequency limit the equalized acoustic resistance box will perform similarly to an equalized two driver plus delay cardioid or a 3 driver cardioid (eq'ed dipole plus monopole).
Look at this image:
An externally hosted image should be here but it was not working when we last tested it.
This shows the phase of the front and rear response of an acoustic resistance enclosure (U-frame) before the resistive element is added. The rear respons eis measured at the exit plane. The rear phase has been inverted. Clearly, in this "undamped" case the phase difference between the front and rear is nominally 180 degrees at low frequency and the system would behave as a dipole at low frequency. However, when the correct resistive element is added the result is as shown here
An externally hosted image should be here but it was not working when we last tested it.
where it is apparent that a constant time delay has been introduced at low frequency by the resistive element. (Maybe it's not so clear, but if I remove a constand time delay from the rear response it will over lay the front exactly up to a little more than 70 Hz. )
The resulting equalized response is as shown here:
An externally hosted image should be here but it was not working when we last tested it.
which also clearly shows that if anything, the cancelation at the rear is improving as the frequency decreases yieldsing a better cardioid response.
No I haven't.
Etienne
The thing you have to watch out for when talking about decay time is whether is is references to the time it takes to decay x many dB form the peak, or the time it takes to decay below a reference level. The former is independent of excitation level and depends only on the Q or the resonance. The latter is dependent on both Q and the max level of excitation. Another thing to consider is room damping. It is fine to try to smooth the response at low frequency by exciting all the room modes evenly, by what ever means. I would agree with Earl on that. But if the room is perfectly rigid what you end up with is lots of very strong peaks separeated by nulls. If the room boundaries have finite, non zero admittance (damping on wall, etc) then the Q of the resonances will decrease and the peaks will broaden out and overlap potentially yielding a smoother response.
john k... said:
Except that it is impossible to maintain a "delay of an acoustic low pass filter tuned to yield the same delay as W goes to zero."
No material that I know would have this property. And resistive material placed in the rear of a single driver open box will have an EFFECT that goes to zero as w goes to zero. Thus, in any real system, the cardiod of a single driver must go to that of a dipole. In your own data it is obvious that the phase difference from front to rear is going to zero as w goes to zero. (I assume that you have reverse phase here somewhere because the phase difference has to be going to 180°) Thus the cardiod MUST become a dipole in the limit as w goes lower.
Your polar graphs don't prove anything other than the response is falling rapidly at all angles. It would be very hard to tell if the response differences were maintaining a cardiod patern from your data and I submit that they have to be becoming a dipole.
I'm still not clear on your explaination other than the part about assuming that the monopole and cardiod have the same free field response, which requires a lot of electronic modification to maintain, and should be so stated.
I'm also quite curiuos how you get measurements down to 10 Hz.
And why is the output from the rear the same level as the front if there is resistance? And if the resistance is not enough to lower the response then how can there be delay?
If these are all near field measurements then your last plot has to be derived fromm two measurements and not a real single measurement and as such is really a simulation.
All in all John, something in your data just doesn't sit well with me.
If nobody wants to deal with the room problem, the rest is waisted money to me... How could you have a many thousands dollars system and don't spend a cent on acoustic treatment? I guess it is one of the fundament of keeping the hifi business going strong!
Room acoustic is a complex topic, so is building speakers. If you follow the rules of the physic you can achieve pretty nice things! Here again I recommend Alton Everest, Master Handbook of Acoustics. The book is easy to read, no need of a master degree in mathematic and quantum physic here!
First things first, you have to treat the room modes. The goal is to damp them, removing them is impossible... the Toole document has some good tips how to achieve it (from page 24).
Then you treat the room in order to have an even decay time. Here Sabine is your friend for the theoretical part and the RT60 measurements will do the practical part.
At last you treat the reflexions with diffuser and stuff like that. Here 2 schools prevail when it comes to side reflexions, either you absorb and/or diffuse them as much as possible or you don't treat the side walls in order to broaden the soundstage. To me, the first is good when listening to acoustic music with a lot of room ambiance and the second is good for studio music on the dry side. So it is pretty much dependent on what you listen to. But here you can have it both if you build (or buy) double face panels, one side is diffusive and the other is reflective!
If you don't treat your room in this order (damp room modes, achieve an even decay time, treat reflexions) you will never get it right.
That's it for the OT about room acoustics!
About John example. First thanks john for posting some figures! Then I would say that there is no need debating about what happens at DC, we will never go there! It is only of academic interest.
I agree with Earl that the absorbent material will be less and less effective as the frequency lowers. This is actually correlated by the graph John posted: the internal delay decreases when the frequency lowers. So that this type of construction behave as a cardioid at the top frequencies and shifts slowly to dipole when the frequency goes down. There will then be no room pressurisation below the room lowest mode, which by the way has little interest to me since my room's lowest mode is at 26Hz and I could live happily with this as the lowest tone my system could reproduce!
Earl, I would like to ask you what kind of drivers do you recommend for a low frequency closed box application. When you put a driver in a box, the resonance frequency goes up so that you need a driver with very low Fs. Then the bigger the volume of the box, the lower you can go (to make a long story short...) but the bigger the volume, the more box resonance you get. No free lunch here... in my case I would like the to have the low frequency speaker between 100 to 300 Hz and down to a solid 40Hz and why not 26Hz! I would like to mention that I am not a big fan of equalisation.
Regards,
Etienne
Room acoustic is a complex topic, so is building speakers. If you follow the rules of the physic you can achieve pretty nice things! Here again I recommend Alton Everest, Master Handbook of Acoustics. The book is easy to read, no need of a master degree in mathematic and quantum physic here!
First things first, you have to treat the room modes. The goal is to damp them, removing them is impossible... the Toole document has some good tips how to achieve it (from page 24).
Then you treat the room in order to have an even decay time. Here Sabine is your friend for the theoretical part and the RT60 measurements will do the practical part.
At last you treat the reflexions with diffuser and stuff like that. Here 2 schools prevail when it comes to side reflexions, either you absorb and/or diffuse them as much as possible or you don't treat the side walls in order to broaden the soundstage. To me, the first is good when listening to acoustic music with a lot of room ambiance and the second is good for studio music on the dry side. So it is pretty much dependent on what you listen to. But here you can have it both if you build (or buy) double face panels, one side is diffusive and the other is reflective!
If you don't treat your room in this order (damp room modes, achieve an even decay time, treat reflexions) you will never get it right.
That's it for the OT about room acoustics!
About John example. First thanks john for posting some figures! Then I would say that there is no need debating about what happens at DC, we will never go there! It is only of academic interest.
I agree with Earl that the absorbent material will be less and less effective as the frequency lowers. This is actually correlated by the graph John posted: the internal delay decreases when the frequency lowers. So that this type of construction behave as a cardioid at the top frequencies and shifts slowly to dipole when the frequency goes down. There will then be no room pressurisation below the room lowest mode, which by the way has little interest to me since my room's lowest mode is at 26Hz and I could live happily with this as the lowest tone my system could reproduce!
Earl, I would like to ask you what kind of drivers do you recommend for a low frequency closed box application. When you put a driver in a box, the resonance frequency goes up so that you need a driver with very low Fs. Then the bigger the volume of the box, the lower you can go (to make a long story short...) but the bigger the volume, the more box resonance you get. No free lunch here... in my case I would like the to have the low frequency speaker between 100 to 300 Hz and down to a solid 40Hz and why not 26Hz! I would like to mention that I am not a big fan of equalisation.
Regards,
Etienne
gedlee said:
The resistive element is a fluid resistance. It must have the characteristic that:
(P1 -P2) = Rf x Q
where (P1 -P2) is the pressure drop across the element and Q is the flow rate, or volume velocity. Simple laminar flow in a pipe has this characteristic: Rf = 128 x ì x L/(Pi x d^2). The problems don't arise until we get to higher frequencies, where, for example with pipe flow, the wave length is on the order of the pipe length.
But, from a practical point of view, it is rather unimportant what happens as DC is approached. I'm not particularly concerned with what happens below 10 Hz when the system is build.
My plots don't show anything? You are kidding, right? The 90 degree response, below 70 Hz is consistently 6dB below the on axis; = cardioid. The rear response is nominally 15 to 20 dB below the on axis response in that region with the difference increasing as the frequency decreases. This is clearly cardioid behavior, and showing an improved tendency towards the cardioid as the frequency decreases. If this were tending to a dipole the 90 degree off axis would tend to null relative to the on axis response and the rear response would be rising to meet the on axis response.
I don't know how I could make the other points much clearer. The eq is not very complex. It's just the inverse of the native 1st order roll off of the gradient system. Big deal! The previous point was that of course you can't maintain that eq to DC as it would require infinite gain. But if you target a 3rd order acoustic roll off and build the dipole or cardioid using sealed box woofers (with 2nd order roll off) then you need only maintain the eq to a specified frequency. The eq becomes an LP shelving function, nothing complex. For example if you target a B3 response at Fp then start with a sealed woofer with a 2nd order, Q = 1, Fp alignment as the sources for the dipole/cardioid and curtail the eq at Fp. The dipole component or the two driver cardioid will have the Fp, B3 roll off. Nothing very complicated there.
Yes, the measurements are near filed and I took some liberty in the plots when overlaying the SPL data because the point was to show the symmetry of the front and rear response and the effect of the damping on the resonance peak. In reality the rear is attenuated, but only by 1 dB or so, which is consistent with the last plots.
I would prefer to call the last plots summations as they are a simple vector sum of the front and rear DATA accounting to the physical path length differences which would exist in a far field, anechoic measurement. Last I heard vector summation of two sources given amplitude and phase was a pretty reliable operation.
As for not sitting well with you, no offence but that seems to be a consistent theme. You don’t like it, so what? I didn't invent the acoustic resistance box; I'm not the only one who uses it for woofer systems; and from everything I have seen, read, built and measured, they are very capable of performing as advertised over any reasonable frequency range.
Etienne88 said:
As you can see from reading my last post, I agree. DC is irrelevant.
As I stated in my last post I don't agree. The delay remains quite constant at low frequency. I made this point verbally in the first post with the plots. I well show it here. Here is the plot of the damped U-frame from the previous post:
An externally hosted image should be here but it was not working when we last tested it.
Here is the exact same data plotted with a constant delay, equal to L/C where L is the length of the U-frame and C the speed of sound, added to the front response:
An externally hosted image should be here but it was not working when we last tested it.
We can argue about the relative amplitudes of the front and rear response at low frequency. As I said in the previous post in response to Earl, I overlaid them to focus on the behavior of the response in the region of the rear resonance. But these two plots make it undeniably clear that below 70 Hz the difference in the front and rear phase is a pure and constant time delay. Remember that the rear phase has been inverted so that what this says is that for all practical purposes, when viewed form the rear the front and rear responses are 180 degrees out of phase below 70 Hz. And the only reason there isn’t perfect cancellation at the rear below 70 Hz is because of the differences in amplitude due to attenuation of the rear response. What happens below 10 Hz, as you and I agree, isn't really of any practical concern. But nevertheless, if the delay remains constant to 10 Hz it isn't going to suddenly drop to zero at 9.
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