Sliding target?
Maybe it's time to stop trolling and get back to the subject of the thread.
That's actually really encouraging to hear.
When I've listened to and looked at the design of some commercial speakers I've sometimes wondered whether some of their shortcomings were due to them being designed largely as an engineering exercise (meet these specified target measurements at the target price) without much regard for whether it actually sounds good, or realistic when reproducing music.
That can give the impression to someone looking from the outside in that the designers were perhaps good engineers but not dedicated music lovers, and/or didn't have enough knowledge of psycho-acoustic research.
(Understanding of how we hear and what measurements do and dont matter - good engineering with the wrong target goals will still give a bad result, for example, flat response, yes, but measured how and in what conditions ?)
From what you say its more likely that budgetary constraints and marketing driven decisions are more to blame and most of the engineers (at least in reputable manufacturers) actually are music lovers and driven by a passion to do a better job at reproducing music.
I know for myself as a DIY'er that I am driven by a love of music and more specifically how the music sounds, I find listening to a really outstanding reproduction of a well engineered recording quite thrilling, even if its a genre of music that doesn't necessarily interest me. (In other words I get just as much enjoyment out of the technical quality and realism of the reproduction of the recording as I do out of the musical content)
Striving to do a better job at the reproduction part of the process (speakers and room interaction) is what pushes me to constantly experiment and learn as much as I can, with discussions on forums like this being a valuable part of that.
It's certainly something I would love to do as a job given the chance, however in this recession I'm lucky if I even have any job at all!
Ah, the famous speaker dave dead pan sarcasm 😀
I have by pointing out the larger context which is that optimizing the mass spring dashpot model is not nearly sufficient by itself to achieve the goal of high fidelity sound reproduction. I'm sorry if that is heretical to a particular religion.
Getting on topic, a suggestion, first separate the issue of “realistic sound”, from the physics of how drivers work and what is required to make the speaker be faithful to the input signal.
A first step would be to correct the driving assumption, a simple woofer lets say, is like a mass and spring, it has a resonant frequency, which in the case of a normal sealed box woofer, is tied to its low frequency corner.
That resonance is damped too, the system is driven by a low impedance source through a resistance.
The spring and mass are reactive elements, they store energy, one as kinetic and the other potential. Electrically they appear to be reactances as well, capacitance as mass and the spring as a parallel inductance.
When they are equal but opposite, like any LC parallel tank circuit, the two cancel each other out and this is where an impedance peak is found.
It is the custom to assign relative Q values to the behavior and here the magnitude of the damping can be seen
When the driver is un-terminated, the air load and mechanical losses are the only damping and this is evident in the Qm of the driver.
Fwiw When I was making transducers for acoustic levitation, I would occasionally test these in a vacuum which removed all the air loads, leaving mechanical losses only in the impedance. That was important because they had a high Q in order to be efficient, one could produce 155 dB (threshold of levitation) at 22KHz with about 20 electrical watts.
When connected to an amplifier (which looks like a short to the speaker with no signal) the electrodynamic damping (see earlier motor explanation) greatly lowers the Q and is in parallel with the Qm the result is the Qt. Several suggested tapping on the cone and observing the difference when you short it’s terminals, a great demo of this!
You put the speaker in a sealed box and now the spring part has a box compliance (spring) in parallel with the suspension and that raises the resonant frequency to be Fb.
In a sealed box, the normal goal is to raise the resonance (which also raises the Q) until the shape of the acoustic response corner is between about .5 and 1 depending on the use.
The mass and spring analogy falls short here because this would appear to describe a mound or band pass response and it does exactly IF what you’re looking at is the radiator velocity.
The problem is that a woofer is usually on the sloped part of the radiation resistance curve and so to get flat response, the velocity must fall off with increasing frequency. That correction slope is provided by the woofers moving mass of the resonant system above it’s resonance dominating the system. Here is a copy of that curve, last curve here;
Loudspeakers
Another way to look at it is if you think in terms of velocity like a car, then you have a rising response with increasing frequency if you have a woofer that is acoustically small, that is to say, when on the sloped part of the curve, a 6 dB per octave correction is required.
On the other hand, the object of a low frequency horn or any horn which seeks efficiency is to connect the acoustically small driver to the part of the curve where the load stops changing. That knee is the ideal mouth size because above that size there is no gain in a larger horn.
Also, when driving that flat part of the curve, what is required now IS velocity and now increasing mass really does roll off the high frequency corner. That is why horn drivers generally have a much larger /stronger motor relative to the radiator area. As the frequencies climb into the tweeter range we find that even the best compression drivers have a velocity roll off, a really good one inch it would be around 3 to 4 KHz. Above that, the acoustic power rolls off and if one has a Constant directivity horn, then that roll off must be compensated to get flat response.
Anyway, some random thoughts while waiting for some measurements to come in.
Best,
Tom Danley
A first step would be to correct the driving assumption, a simple woofer lets say, is like a mass and spring, it has a resonant frequency, which in the case of a normal sealed box woofer, is tied to its low frequency corner.
That resonance is damped too, the system is driven by a low impedance source through a resistance.
The spring and mass are reactive elements, they store energy, one as kinetic and the other potential. Electrically they appear to be reactances as well, capacitance as mass and the spring as a parallel inductance.
When they are equal but opposite, like any LC parallel tank circuit, the two cancel each other out and this is where an impedance peak is found.
It is the custom to assign relative Q values to the behavior and here the magnitude of the damping can be seen
When the driver is un-terminated, the air load and mechanical losses are the only damping and this is evident in the Qm of the driver.
Fwiw When I was making transducers for acoustic levitation, I would occasionally test these in a vacuum which removed all the air loads, leaving mechanical losses only in the impedance. That was important because they had a high Q in order to be efficient, one could produce 155 dB (threshold of levitation) at 22KHz with about 20 electrical watts.
When connected to an amplifier (which looks like a short to the speaker with no signal) the electrodynamic damping (see earlier motor explanation) greatly lowers the Q and is in parallel with the Qm the result is the Qt. Several suggested tapping on the cone and observing the difference when you short it’s terminals, a great demo of this!
You put the speaker in a sealed box and now the spring part has a box compliance (spring) in parallel with the suspension and that raises the resonant frequency to be Fb.
In a sealed box, the normal goal is to raise the resonance (which also raises the Q) until the shape of the acoustic response corner is between about .5 and 1 depending on the use.
The mass and spring analogy falls short here because this would appear to describe a mound or band pass response and it does exactly IF what you’re looking at is the radiator velocity.
The problem is that a woofer is usually on the sloped part of the radiation resistance curve and so to get flat response, the velocity must fall off with increasing frequency. That correction slope is provided by the woofers moving mass of the resonant system above it’s resonance dominating the system. Here is a copy of that curve, last curve here;
Loudspeakers
Another way to look at it is if you think in terms of velocity like a car, then you have a rising response with increasing frequency if you have a woofer that is acoustically small, that is to say, when on the sloped part of the curve, a 6 dB per octave correction is required.
On the other hand, the object of a low frequency horn or any horn which seeks efficiency is to connect the acoustically small driver to the part of the curve where the load stops changing. That knee is the ideal mouth size because above that size there is no gain in a larger horn.
Also, when driving that flat part of the curve, what is required now IS velocity and now increasing mass really does roll off the high frequency corner. That is why horn drivers generally have a much larger /stronger motor relative to the radiator area. As the frequencies climb into the tweeter range we find that even the best compression drivers have a velocity roll off, a really good one inch it would be around 3 to 4 KHz. Above that, the acoustic power rolls off and if one has a Constant directivity horn, then that roll off must be compensated to get flat response.
Anyway, some random thoughts while waiting for some measurements to come in.
Best,
Tom Danley
From the referenced link;
"The smaller the speaker, the poorer its low frequency production."
From my posting #36
"The respective resonance frequencies for the undamped systems is 1/2TT*(sq rt K/M)"
It would seem from the equation by loosening the spring and increasing the mass you could make any size driver have as low a free air resonant frequency as you want it to be. The discrepancy may be in absolute efficiency versus relative efficiency as a function of frequency. The 4" driver that has a free air resonance of 15 hz may not be a very efficient converter of electrical power to acoustic power even though it may have an in box FR flat down to 30 hz or lower. When the cost of amplifier power was a major concern and the cost of multiple drivers was also this might have been a problem. However, for home use where multi-hundred watt amplifiers are a few hundred dollars and speaker drivers are manufactured like cookies are baked in a factory in China the cost equation changes. Why would a single large driver have any advantage over an array of small drivers with the same overall radiating surface area and same moving mass if the maximum excursion was sufficient to produce the desired SPL?
"The smaller the speaker, the poorer its low frequency production."
From my posting #36
"The respective resonance frequencies for the undamped systems is 1/2TT*(sq rt K/M)"
It would seem from the equation by loosening the spring and increasing the mass you could make any size driver have as low a free air resonant frequency as you want it to be. The discrepancy may be in absolute efficiency versus relative efficiency as a function of frequency. The 4" driver that has a free air resonance of 15 hz may not be a very efficient converter of electrical power to acoustic power even though it may have an in box FR flat down to 30 hz or lower. When the cost of amplifier power was a major concern and the cost of multiple drivers was also this might have been a problem. However, for home use where multi-hundred watt amplifiers are a few hundred dollars and speaker drivers are manufactured like cookies are baked in a factory in China the cost equation changes. Why would a single large driver have any advantage over an array of small drivers with the same overall radiating surface area and same moving mass if the maximum excursion was sufficient to produce the desired SPL?
A single round woofer sees a higher radiation resistance at low frequencies than multiple adjacent round woofers whose total summed cone area is the same as the single large woofer.
This is because the mutual coupling between the multiple round woofers is less, (than the coupling between different portions of a single cone) due to the gaps between the radiating cones in an array of circular drivers.
It doesn't affect the required excursion but it does affect the overall efficiency.
A single large driver is generally cheaper to produce, box and ship than a number of small drivers with the same displacement.
The surround width needs to be the same on a small driver as a large driver for the same excursion. A 65 mm driver with a 20mm Xmax would have hardly any actual SD.
Small long excursion drivers devote a much larger percent of the cone area to the surround (compared to large cones), the surround produces little actual SPL output, so small drivers are less efficient use of available area.
All a compromise, too small, little usable cone area, too large and keeping the cone stiff requires it to be heavier, requiring more magnet strength, requiring neodymium to keep weight reasonable, and neo prices are through the roof now.
Soundminded posed;
“It would seem from the equation by loosening the spring and increasing the mass you could make any size driver have as low a free air resonant frequency as you want it to be.”
Yes, at least within a computer model.
What is even more weird, the T&S parameters we all deal with can be optimized for a given box and low corner BUT in that relationship, the Sd is not yet defined. That means that one can derive the same parameters for an 8,10,12,15, 18 or any size woofer (at least theoretically) and with the same box, get the same frequency response. How loud it goes is connected to other parameters like Xmax.
For example, if one had a 3 cu/ft box volume and wanted a classic b4 vented alignment -3dB at 30Hz, the root parameters are;
Fs=30
Qt=.4
Vas=3.18
Sensitivity 89.5 dB
Rdc=5 Ohms (I decided that one)
But no physical parameters are contained here and so “in theory” any size driver could be made with these parameters. Like animating a cartoon real time, this process is a little cumbersome but here are two drivers that would have the same response curve, same sensitivity and have the same T&S parameters.
An 8 inch diameter radiator
BL=10.06
MMS = 46 Gm
CMS = .061 cm /N
A 16.5 inch diameter radiator
BL=42
MMS=835 Gm
CMS = .0034 cm / N
Both of these have the same T&S parameters as listed above!
Large signal parameters are another issue.
Best,
Tom Danley
“It would seem from the equation by loosening the spring and increasing the mass you could make any size driver have as low a free air resonant frequency as you want it to be.”
Yes, at least within a computer model.
What is even more weird, the T&S parameters we all deal with can be optimized for a given box and low corner BUT in that relationship, the Sd is not yet defined. That means that one can derive the same parameters for an 8,10,12,15, 18 or any size woofer (at least theoretically) and with the same box, get the same frequency response. How loud it goes is connected to other parameters like Xmax.
For example, if one had a 3 cu/ft box volume and wanted a classic b4 vented alignment -3dB at 30Hz, the root parameters are;
Fs=30
Qt=.4
Vas=3.18
Sensitivity 89.5 dB
Rdc=5 Ohms (I decided that one)
But no physical parameters are contained here and so “in theory” any size driver could be made with these parameters. Like animating a cartoon real time, this process is a little cumbersome but here are two drivers that would have the same response curve, same sensitivity and have the same T&S parameters.
An 8 inch diameter radiator
BL=10.06
MMS = 46 Gm
CMS = .061 cm /N
A 16.5 inch diameter radiator
BL=42
MMS=835 Gm
CMS = .0034 cm / N
Both of these have the same T&S parameters as listed above!
Large signal parameters are another issue.
Best,
Tom Danley
"Yes, at least within a computer model.
What is even more weird, the T&S parameters we all deal with can be optimized for a given box and low corner BUT in that relationship, the Sd is not yet defined. That means that one can derive the same parameters for an 8,10,12,15, 18 or any size woofer (at least theoretically) and with the same box, get the same frequency response. How loud it goes is connected to other parameters like Xmax."
I'm thinking about building a surface array using about 36 4" to 5" midwoofers per channel in a monopole closed back panel like enclosure. I think it will be very easy to build. A lot of hole saw drilling. I want to test my theory that panel type speakers get their special sound from their large radiating surface, not from anything particularly unique about a low mass membrane instead of an electromagnetic linear motor. It won't take much depth to get a fairly high internal volume. It will be at least a 2 way system with an intermixed corresponding tweeter array.
Popular electonics published an article about a 16 5" table radio driver array back in the early 1960s they called "The Sweet Sixteen. I think they were Jensen, maybe the same or similar to Kloss's first 4 driver effort before he tied up with Villchur and the drivers used in AR2. Bose used 9 4" CTS drivers in his original design. He deliberately pushed Fs above 180 hz. e/e Magazine reported theirs had an 8 db peak at around 250 hz indicating a high Q. Mine seem to be at about 500 hz and a high Q with a peak of around 7db. Response falls off at the predicted 12 db per octave but the equalizer only provides a 6db per octave boost. The system needs another 6db per octave boost to flatten FR, its response crosses 1 Khz output at around 95 hz. This brings the power requirement up from 60 to 250wpc suggested by Bose to 600 to 1000 wpc. The system can only handle 270 so they need to be stacked in multiples of around 3 or 4 pairs. Tom Tyson at CSP claims their Xmax is 5mm but I find that hard to believe. Sd for the aggregate of each channel is the equivalent of a single 14" driver based on my measurements of them, about 2 1/2 inches from outer edge of cone to outer edge across their diameter. Within their power handling capability they're actually good to around 23 to 26 hz. Due to the high intertial mass of the cone the system of course has almost no output in the top octave and what little there is beams on axis of each driver. So without further equalization and an add on tweeter array to provide the top octave there's something to the old saying no highs, no lows, it's Bose, at least for that design.
What is even more weird, the T&S parameters we all deal with can be optimized for a given box and low corner BUT in that relationship, the Sd is not yet defined. That means that one can derive the same parameters for an 8,10,12,15, 18 or any size woofer (at least theoretically) and with the same box, get the same frequency response. How loud it goes is connected to other parameters like Xmax."
I'm thinking about building a surface array using about 36 4" to 5" midwoofers per channel in a monopole closed back panel like enclosure. I think it will be very easy to build. A lot of hole saw drilling. I want to test my theory that panel type speakers get their special sound from their large radiating surface, not from anything particularly unique about a low mass membrane instead of an electromagnetic linear motor. It won't take much depth to get a fairly high internal volume. It will be at least a 2 way system with an intermixed corresponding tweeter array.
Popular electonics published an article about a 16 5" table radio driver array back in the early 1960s they called "The Sweet Sixteen. I think they were Jensen, maybe the same or similar to Kloss's first 4 driver effort before he tied up with Villchur and the drivers used in AR2. Bose used 9 4" CTS drivers in his original design. He deliberately pushed Fs above 180 hz. e/e Magazine reported theirs had an 8 db peak at around 250 hz indicating a high Q. Mine seem to be at about 500 hz and a high Q with a peak of around 7db. Response falls off at the predicted 12 db per octave but the equalizer only provides a 6db per octave boost. The system needs another 6db per octave boost to flatten FR, its response crosses 1 Khz output at around 95 hz. This brings the power requirement up from 60 to 250wpc suggested by Bose to 600 to 1000 wpc. The system can only handle 270 so they need to be stacked in multiples of around 3 or 4 pairs. Tom Tyson at CSP claims their Xmax is 5mm but I find that hard to believe. Sd for the aggregate of each channel is the equivalent of a single 14" driver based on my measurements of them, about 2 1/2 inches from outer edge of cone to outer edge across their diameter. Within their power handling capability they're actually good to around 23 to 26 hz. Due to the high intertial mass of the cone the system of course has almost no output in the top octave and what little there is beams on axis of each driver. So without further equalization and an add on tweeter array to provide the top octave there's something to the old saying no highs, no lows, it's Bose, at least for that design.
I've been thinking about this comment a bit. In the pervious (why 6dB?)thread where we talked about acoustic impedence, mutual coupling and such, I found two references to multiple woofer systems, one from Keele and one from Gander and Eargle. The jist of it was that the gain from multiple woofers would be a combination of efficiency gain or "mutual coupling" gain at lowest frequencies and directivity gain above.
In fact it looked like you could consider multiple woofers on axis as the vector sum of all the sources, i.e. 6dB for each doubling of number of woofers, and the efficiency/directivity gain combination would sort itself out to match. That is gain off efficiency at lower frequencies and gain of directivity at higher frequencies would add to exactly equal the far field in-phase summing of all the elements.
In your multiple spread woofer case then you would be increasing directivity while reducing mutual coupling. i.e. if you had a fill factor of 50% then your area would double, your diameter for the multielement equivalent woofer would go up by 40% and the directivity increase would offset the loss in efficiency gain.
This seems to be the case but is it as simple as that?
David S.
In phase coupling at higher frequencies would add to 6dB and out of phase would cancel. Directivity gain is a colourful (to me) way to put it. Power response would be reduced. It would seem that it's the same at all frequencies only the lower ones will combine cleanly.
Not being colorful but refering to increase in directivity index. At higher frequencies the gain off axis will be less due to cancellation, the polar curve would reflect it so the d.i. or Q would be greater. At frequencies where wavelengths are such that the gain applies to all angles then it will be a power response gain and so the acoustic impedance must have risen, i.e. mutual coupling is happening.
The relationship appears to be:
axial gain = power response gain + d.i. gain
(all a function of frequency)
David S.
The relationship appears to be:
axial gain = power response gain + d.i. gain
(all a function of frequency)
David S.
The notion of comb filtering always comes up with multidriver arrays. But in a large surface array the number of comb filters grows quickly. The number of combs and their physical locations is (N-1)! because each additional driver creates a new one with every other driver. for 36 of them for example the number is so large, 35!, the importance of any one of them to the aggregate field becomes so small, and each pair different from the others that for all practical intents and purposes they no longer exist. Also Bose pointed out that with just 9 drivers the minor variations in FR from unit to unit also become insignificant. This allowed him to equalize for the average curve (even if he got it wrong in his production units), the FR much smoother (if not flat) than any one of them individually.
For small arrays, yes it is just the vector sum. But for larger arrays not so because by doubling and doubling again, and again.... you very quickly find that efficiency at low frequency goes over 100%. 😱 I'm sure Tom can explain this better than me.
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But surely as the array of speakers increased in number and size a point is reached where it becomes directional even at low frequencies. Then the axial gain is being achieved through directivity increase not increases in actual efficiency. (I think that's Dave's point)
Just because the on axis response is continuing to increase 6dB per doubling of drivers doesn't mean the power response has gone over unity.
Another thing to remember is that doubling the number of drivers increases the output by 6dB on axis but you are also increasing the drive power by 3dB since each driver is driven by the same power that an individual driver previously was. (eg one driver driven by 1 watt, vs 2 drivers each driven by 1 watt)
So the actual increase of efficiency based on power input to SPL output is only 3dB per doubling of drivers.
Correction, the actual increase in axial SPL from a doubling of drivers for the same total input power is 3dB. And if Dave's idea is right then at low frequencies and/or small arrays its coming mostly from mutual coupling, and at higher frequencies and/or larger array sizes its coming mostly from directivity increase.
Ok, now my head hurts 😛
In a sealed enclosure coupling is excellent.This is where the mass spring dashpot shows great advantage. Multiple small masses on multiple small springs and dashpots all tied together. Changes in air pressure inside the box at any point translates to corresponding changes at every other point very quickly. Push in on any driver in an original or series II Bose 901 that's properly sealed and the other 8 pop out simultaneously and seemingly instantly. Release it and the other 8 return just as quickly. Easy way to check for an air leak. Same thing happens with Teledyne AR9's two sealed 12" subwoofers.
This is not what we're referring to.
The mutual coupling between two adjacent woofers is the loading that each woofer sees from the other due to the external air pressure difference.
Whether you have two side by side woofers sharing the same 50 litre box, or two side by side woofers each in their own separate 25 litre enclosures makes no difference to the loading each woofer sees due to the others presence.
(In the shared box case the back pressure from each woofer cancels out, so each woofer only "sees" half the total box volume)
That flies in the face of both theory and practical experience. The back pressure wave of one driver directly affects the others, far more so than what's in front of the driver which is in the external air where the change in atmospheric pressure locally is much smaller. Proof? Two AR3 type woofers in separate enclosures have an F3 of 42 hz individually or in adjacent pairs. Same two drivers in a single double sized enclosure, AR9 have an F3 of 28 hz. See Tim Holl's excellent writeup in CSP's Library.
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