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#1
Posted to rec.audio.high-end
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Cylindrical vs. box shaped subwoofers
"Barkingspyder" wrote in message
... Are there any advantages other than a smaller foot print for cylindrical subwoofers? Do they require damping material in the same way a box would? I'm considering a DIY project and would be curious as to the science on this topic. Are there the same problems with vibrations inside the enclosure, or does the cylinder reduce or make them a non-issue? I see a lot of the sonotube desgins have the driver at one end and he port at the other. Does it make any difference if they are are at the same end of the tube assuming a large enough diameter? I am considering a 143 L EBS alignment with both the port and the driver at the bottom. The tube would be 20" in diameter and a 4" port. I am not married to these dimensions but I thought there would be a higher WAF if the thing looked less like a water heater. Comments please. Hi Barking - Some comments from a friend: "Well, in theory a box-shaped sub enclosure will try to flex its wall inward or outward as the cone moves in and out, with the idea being that the pressure is trying to turn the box into a sphere. A cylinder-enclosure shape, even with the cylinder walls only 3/8 inch thick, cannot flex inward or outward (assuming the Sonotube fiber material is decently strong in terms of stretch resistance, and believe me, Sonotube is strong), because the surface is already curved to a circle. Yes, it is not a sphere, but the top plate cannot flex outward or inward, because it is mostly filled with the driver, and the bottom plate cannot flex much, because it has the port tube in there reinforcing it and the thing is usually too thick to flex much, anyway. My bottom plates are each 2.25 inches thick, for example, with the bottom plate itself standing on 3-inch pegs that themselves are screwed to still another bottom plate. (There is a similar standoff plate on the top that is there simply for cosmetic purposes and to protect the driver cone.) The inside of the Sonotube should be layered with a couple of inches of fiberglass (mine is held in place with 3M spray adhesive, and the fiberglass is actually furnace pipe wrap with the foil removed), and the idea there is for the heating and cooling of the fiberglass under pressure (which can occur at any frequency above the port resonance) to help the driver to "see" a larger interior space than is actually there. (Acoustic-suspension woofers and subwoofers also have something like that in their cabinet interiors for the same reason.) The effect is actually minimal, but in any case the fiberglass is not there to control resonances or absorb noise. Resonances are minimal with a cylinder enclosure, actually, due to the lack of glued-together speaker-wall joints. In any case, in practical terms, a Sonotube enclosure should be the most resonant-free enclosure possible for a subwoofer, although the light weight is a theoretical problem - that I have not encountered. It really does not matter where the port is, although it can if the woofer/port interface is not quite right.and the driver and port are side by side The first successful commercial sub Poh Ser Hsu made was a pretty fat cylinder and both the driver and the port were on the bottom. Later Hsu models like the TN1220 had the driver at one end and the port at the other, as did (and do) the SVS cylinder models. Ditto for the units I made for my main audio system. If the port and driver are on the bottom, the designer can have an attractive top on the cabinet that will allow it to function as an end table, or the like. However, the light weight of a sonotube enclosure will allow the entire unit to vibrate up and down, which might make that table lamp dance around a bit. There obviously is an advantage to a smaller footprint with a tall, skinny design, if floor space is critical, but of course what you gain in in terms of left-over floor space you lose in terms of space above the unit. No free lunch there, particularly if the wife does not like to see cylinder-sub towers rising towards the ceiling. (Fortunately, my wife may actually like the looks of my units.) What can matter when it comes to how low the sub can go, in additon to port-tube length and diameter (and of course driver design), is the interior space of the enclosure. There are web-sites out there that help the user to calculate both interior cabinet space with a cylinder (square inches of circular area can be calculated with one site; times length of Sonotube) as well as the required tube length and diameter with a given enclosure space and desired tuning frequency. The calculating can be done in less than a minute, actually. Once that math work is done, all one need do is order the parts (the driver, the Sonotube, which comes in 12-foot lengths and obviously has to be cut down, mdf to make end plugs, port-tube materials, screws, glue, and grill fabric). You need the grill fabric to wrap around the finished product to keep it from looking, as the poster noted, like a black-painted water heater, tall or short. Heck, grill cloth comes in a variety of colors and one can even go to a fabric store and look through all sorts of nifty designs. A bright red cylinder sub would look really cool. Mine are both black, however, in keeping with tradition. Note that the pair in my main room are now using 12-inch, Dayton Reference Series drivers instead of the 12-inch, DaytonTitanic drivers I first tried. They go down to the bottom end a bit smoother than the Titanics (although theoretically they cannot play as loud, but can play plenty loud enough) and have less cone-flex noise. The full systems are 68 inches tall and 14 inches in diameter, although the Sonotubes themselves are only 56 inches tall (the additonal 12 inches involve end plugs and standoff bottom and top plates), giving they an interior volume of 5 cubic feet. This allows tuning to 19 Hz, and to keep things really smooth I equalize the bottom seven 1/3-octave points with an ART EQ-351 equalizer. The result is the best sub-extension measurements I have encountered in that room. Power for the two subs, as I may have noted before, is via a Crown XLS1000 digital D class, 700-watt power amp. This is not a super-low distortion amp, but it is more than adequate for sub driving, and has RCA jacks for an easy interface with a consumer-grade receiver sub-out hookup. Seven hundred watts is way, way more power than I need (the room is 3400 cubic feet, and the amp/sub pair combo can give me 115 dB at 30 Hz with ease, and almost as much at 20 Hz), but I got the amp cheap from Parts Express. The damned amp weighs less than 9 pounds (each cylinder sub weighs in at about 50 pounds, including driver, by the way, making them featherweights in the super-sub sweepstakes), and it has a cooling fan that is so silent that you have to put your ear against the front panel to hear it running. I plan on building two more for my AV system in the back area, using the now spare Titanic drivers (which are better for home theater, anyway, than the Reference units), mounted in same diameter enclosures as what I have in the main room, but with a height of 58 inches. They will be tuned to about 24 Hz - proper enough for home-theater use. A second Crown XLS1000 will do the powering work, and I will use an existing Rane THX-44 and outboard Hsu "Optimizer" equalizer to fine-tune the response smoothness and extension." End quote. Gary Eickmeier |
#2
Posted to rec.audio.high-end
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Cylindrical vs. box shaped subwoofers
Gary Eickmeier wrote:
"Well, in theory a box-shaped sub enclosure will try to flex its wall inward or outward as the cone moves in and out, with the idea being that the pressure is trying to turn the box into a sphere. Several things poop into my head when I read this: "What's the difference between theory and practice? In theory, theory and practice are the same. In practice, theory and practice are different." It's on the Internet, so it must be true. A cylinder-enclosure shape, even with the cylinder walls only 3/8 inch thick, cannot flex inward or outward (assuming the Sonotube fiber material is decently strong in terms of stretch resistance, and believe me, Sonotube is strong), because the surface is already curved to a circle. Oh, be assured, kind people, it most assuredly can and quite happily does. The assertion that it cannot is based on the following assumptions: 1. That the wall material is infinitely rigid, has infinite tensile strength, i.e., it can neither be stretched, compressed or flexed. The 3/8" cardboard walls of a Sonotube are VERY VERY far from that ideal, 2. That the internal forces on the walls are the same at every point along the walls surface. With ANY musical material, this is simply not the case. 3. That the cylinder is infinitely long, i.e., it has no boundary conditions to deal with. Again, not the case "in practice." Consider two cyclinders of MUCH greater strength than that of a 20" Sonotube: the walls of the SRMs on a shuttle were 1/2" steel. The ignition transient was predicted and was measured to cause the walls halfway between the field joints to expand nearly a foot. But because the field joints used a much heavier, thicker steel ring, they did not bulge anywhere near that much. The result was phenomenon called "joint rotation" and was crucial to causing the failure of the field joints in the Challenger explosion. Be that as it may, while "in theory" it seems like Sonotube is an "ideal" way of building a subwoofer, "in practice"m most of those teoretical advantages simply aren't there. I had, for a former client, done quite a bit of measurements on cardboard tube enclosure, most of which were MUCH more substantial than Sontotube (minimum 3/4" wall thickness, higher density wrap). Using acceelerometer measurements, wall flexing was NO better and most of the time WORSE than a rectangular enclosure of the same corss-sectional are. The unsuported walls of the rectangular enclosure did no worse under the same conditions, and at the corners, they behaved MUCH better. At freuqencies where the wavelengths were smaller than either the length or cricumerance of the tube, cyclinders tid MUCH worse in almost every respect. We would see nodal vibration patterns on the wall that had very high Q'. This is directly attributable to the very dimensional symmetry of the shape. Siply because the unsupported area of the "soundboard" was now the length of the enclosure times its circumference: nodal patterns could be easily set up and well established at MUCH lower frequencies than in a similarly dimensioned rectangula enclosu the largest unsupported surface in a box is substantially smaller than that of the cylinder. And the argument that "A cylinder-enclosure shape ... cannot flex inward or outward" Makes the simplifying and quite incorrect assumption that there's a single, in phase constant force on every square cm of its curface, annd thus the wall MUST be compelled to move uniformly radially. Sorry, but that just doesn't happen in loudspeaker enclosures. TO get the walls to fles very nicely, all you have to do is get it going outward at one point atv the same time it's going inward womehere else along its circumference. And, as far as local stiffness is concerned, Sonotube ain't so hot, especially 3/8" Sonotube. If you want to deal with this issue, consider getting TWO sonotubes, on loerger in diameter (by maybe 1-2"): place them concentrically and then fill in the space between the two with something heavy and mechancially lossy, like dry sand (or, uhm, concrete!). Yes, it is not a sphere, but the top plate cannot flex outward or inward, because it is mostly filled with the driver, and the bottom plate cannot flex much, because it has the port tube in there reinforcing it and the thing is usually too thick to flex much, anyway. Wanna bet? The port tube DOES NOT reinforce it: the hole, in fact, weakens it. My bottom plates are each 2.25 inches thick, Okay, so you "cheated." They don't flex because they are round, or because they have a driver, or becasue they have a port, they don't flex merely because they are 2 1/4" thick. The inside of the Sonotube should be layered with a couple of inches of fiberglass (mine is held in place with 3M spray adhesive, and the fiberglass is actually furnace pipe wrap with the foil removed), and the idea there is for the heating and cooling of the fiberglass under pressure (which can occur at any frequency above the port resonance) to help the driver to "see" a larger interior space than is actually there. (Acoustic-suspension woofers and subwoofers also have something like that in their cabinet interiors for the same reason.) The effect is actually minimal, but in any case the fiberglass is not there to control resonances or absorb noise. Resonances are minimal with a cylinder enclosure, actually, due to the lack of glued-together speaker-wall joints. Sorry, the very axial and radial symmetry means they have the ability to suport quite nasty, highQ resonance. Take a glass pie plate, fill it with water, and put a speaker near it, driven by an oscillator: you'll find any enclosure with a circular cross section support standing wave VERY nicely. Or, for a dramatic acoustical demonstration of the effect, toss a fire cracker into a cylinfrical storm drain: it doesn't go bang! it goes Bonnnnnnnggggggg! for a VERY long time. And, surprise, you find that the pitch of the bong! it inversely proportional to its diameter. And a cylinder also supports end-to-end standing waves quite nicely as well. That's why flute, organ pipes and such are made, largely, of cylinders. In any case, in practical terms, a Sonotube enclosure should be the most resonant-free enclosure possible for a subwoofer, although the light weight is a theoretical problem - that I have not encountered. Sorry, both theory and practice demonstrate otherwise. If the port and driver are on the bottom, the designer can have an attractive top on the cabinet that will allow it to function as an end table, or the like. And has a problem in calculating what the effective radiation impedance seen by both the port and the driver a rest assured, if you assume that it has no effect, you'll get it wrong. However, the light weight of a sonotube enclosure will allow the entire unit to vibrate up and down, which might make that table lamp dance around a bit. Please, do we have to bust this myth AGAIN (or did we miss the smiley)? Assume the mass of the driver cone is, oh 200 grams. Assume also that the driver, enclosure and lamp together weigh 30 kilograms. By conservation of momentum calculate what the worst case "bouncing" of the lamp will be. Show your work. Get back to us when you have an answer. -- +--------------------------------+ + Dick Pierce | + Professional Audio Development | +--------------------------------+ |
#3
Posted to rec.audio.high-end
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Cylindrical vs. box shaped subwoofers
On Mon, 16 Jul 2012 06:59:04 -0700, Gary Eickmeier wrote
(in article ): "Barkingspyder" wrote in message ... Are there any advantages other than a smaller foot print for cylindrical subwoofers? Do they require damping material in the same way a box would? I'm considering a DIY project and would be curious as to the science on this topic. Are there the same problems with vibrations inside the enclosure, or does the cylinder reduce or make them a non-issue? I see a lot of the sonotube desgins have the driver at one end and he port at the other. Does it make any difference if they are are at the same end of the tube assuming a large enough diameter? I am considering a 143 L EBS alignment with both the port and the driver at the bottom. The tube would be 20" in diameter and a 4" port. I am not married to these dimensions but I thought there would be a higher WAF if the thing looked less like a water heater. Comments please. Hi Barking - Some comments from a friend: "Well, in theory a box-shaped sub enclosure will try to flex its wall inward or outward as the cone moves in and out, with the idea being that the pressure is trying to turn the box into a sphere. A cylinder-enclosure shape, even with the cylinder walls only 3/8 inch thick, cannot flex inward or outward (assuming the Sonotube fiber material is decently strong in terms of stretch resistance, and believe me, Sonotube is strong), because the surface is already curved to a circle. Yes, it is not a sphere, but the top plate cannot flex outward or inward, because it is mostly filled with the driver, and the bottom plate cannot flex much, because it has the port tube in there reinforcing it and the thing is usually too thick to flex much, anyway. My bottom plates are each 2.25 inches thick, for example, with the bottom plate itself standing on 3-inch pegs that themselves are screwed to still another bottom plate. (There is a similar standoff plate on the top that is there simply for cosmetic purposes and to protect the driver cone.) The inside of the Sonotube should be layered with a couple of inches of fiberglass (mine is held in place with 3M spray adhesive, and the fiberglass is actually furnace pipe wrap with the foil removed), and the idea there is for the heating and cooling of the fiberglass under pressure (which can occur at any frequency above the port resonance) to help the driver to "see" a larger interior space than is actually there. (Acoustic-suspension woofers and subwoofers also have something like that in their cabinet interiors for the same reason.) The effect is actually minimal, but in any case the fiberglass is not there to control resonances or absorb noise. Resonances are minimal with a cylinder enclosure, actually, due to the lack of glued-together speaker-wall joints. In any case, in practical terms, a Sonotube enclosure should be the most resonant-free enclosure possible for a subwoofer, although the light weight is a theoretical problem - that I have not encountered. It really does not matter where the port is, although it can if the woofer/port interface is not quite right.and the driver and port are side by side The first successful commercial sub Poh Ser Hsu made was a pretty fat cylinder and both the driver and the port were on the bottom. Later Hsu models like the TN1220 had the driver at one end and the port at the other, as did (and do) the SVS cylinder models. Ditto for the units I made for my main audio system. If the port and driver are on the bottom, the designer can have an attractive top on the cabinet that will allow it to function as an end table, or the like. However, the light weight of a sonotube enclosure will allow the entire unit to vibrate up and down, which might make that table lamp dance around a bit. There obviously is an advantage to a smaller footprint with a tall, skinny design, if floor space is critical, but of course what you gain in in terms of left-over floor space you lose in terms of space above the unit. No free lunch there, particularly if the wife does not like to see cylinder-sub towers rising towards the ceiling. (Fortunately, my wife may actually like the looks of my units.) What can matter when it comes to how low the sub can go, in additon to port-tube length and diameter (and of course driver design), is the interior space of the enclosure. There are web-sites out there that help the user to calculate both interior cabinet space with a cylinder (square inches of circular area can be calculated with one site; times length of Sonotube) as well as the required tube length and diameter with a given enclosure space and desired tuning frequency. The calculating can be done in less than a minute, actually. Once that math work is done, all one need do is order the parts (the driver, the Sonotube, which comes in 12-foot lengths and obviously has to be cut down, mdf to make end plugs, port-tube materials, screws, glue, and grill fabric). You need the grill fabric to wrap around the finished product to keep it from looking, as the poster noted, like a black-painted water heater, tall or short. Heck, grill cloth comes in a variety of colors and one can even go to a fabric store and look through all sorts of nifty designs. A bright red cylinder sub would look really cool. Mine are both black, however, in keeping with tradition. Note that the pair in my main room are now using 12-inch, Dayton Reference Series drivers instead of the 12-inch, DaytonTitanic drivers I first tried. They go down to the bottom end a bit smoother than the Titanics (although theoretically they cannot play as loud, but can play plenty loud enough) and have less cone-flex noise. The full systems are 68 inches tall and 14 inches in diameter, although the Sonotubes themselves are only 56 inches tall (the additonal 12 inches involve end plugs and standoff bottom and top plates), giving they an interior volume of 5 cubic feet. This allows tuning to 19 Hz, and to keep things really smooth I equalize the bottom seven 1/3-octave points with an ART EQ-351 equalizer. The result is the best sub-extension measurements I have encountered in that room. Power for the two subs, as I may have noted before, is via a Crown XLS1000 digital D class, 700-watt power amp. This is not a super-low distortion amp, but it is more than adequate for sub driving, and has RCA jacks for an easy interface with a consumer-grade receiver sub-out hookup. Seven hundred watts is way, way more power than I need (the room is 3400 cubic feet, and the amp/sub pair combo can give me 115 dB at 30 Hz with ease, and almost as much at 20 Hz), but I got the amp cheap from Parts Express. The damned amp weighs less than 9 pounds (each cylinder sub weighs in at about 50 pounds, including driver, by the way, making them featherweights in the super-sub sweepstakes), and it has a cooling fan that is so silent that you have to put your ear against the front panel to hear it running. I plan on building two more for my AV system in the back area, using the now spare Titanic drivers (which are better for home theater, anyway, than the Reference units), mounted in same diameter enclosures as what I have in the main room, but with a height of 58 inches. They will be tuned to about 24 Hz - proper enough for home-theater use. A second Crown XLS1000 will do the powering work, and I will use an existing Rane THX-44 and outboard Hsu "Optimizer" equalizer to fine-tune the response smoothness and extension." End quote. Gary Eickmeier I don't think the subwoofer cares about the shape of the enclosure as long as it's as inert as possible and the volume is sufficient and you do the port maths correctly. You don't want the subwoofer enclosure to flex no matter what shape it is. I once built a subwoofer from a piece of oval ceramic fireplace chimney flue-liner pipe. I cut two 3/4" pieces of plywood to fit on each end of the 3 ft flue-liner section. I cut an oval hole in one end to take the odd-looking British KEF low frequency driver that was popular in those days, and after measuring the inside dimensions of the "enclosure", figured the bass reflex port size after Hoge and Bullock, and used four long, threaded rods to clamp the end pieces onto the pipe after lining the pipe with fiberglass insulation. The threaded rods extended about three inches beyond the end with the driver attached and these served as legs to keep the driver off the floor. I painted the flue liner pipe and the end baffles black. It worked fine and I used it for many years with good results. I was getting good bass down into the low thirties from that KEF driver. |
#4
Posted to rec.audio.high-end
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Cylindrical vs. box shaped subwoofers
Barkingspyder wrote:
Gary Eickmeier wrote: The inside of the Sonotube should be layered with a couple of inches of fiberglass (mine is held in place with 3M spray adhesive, and the fiberglass is actually furnace pipe wrap with the foil removed), and the idea there is for the heating and cooling of the fiberglass under pressure (which can occur at any frequency above the port resonance) to help the driver to "see" a larger interior space than is actually there. While all the words are sorta right, they're assembled in a way that, well, falls a wee bit short of the mark, If you have the advantages of the curved shape and you have the right internal volume to begin with, ( I'll be using 143 liters with a Shiva MKII 12" woofer) what actual need if any for the the fiberglass? As to fiberglass I would be hesitant about using it in a ported enclosure since the notion of fiberglass being pumped into the air from the port does not appeal to me. It just seems to me that in 5 cu ft there is little chance of much heat developing, so little need for cooling. Actually, it's not about "insulating" to keep the heat down. Sound, as it turns out when you follow it down to its physical underpinnings, is simply a thermodynamic phenomenon. ALL sound must, at its very root, involve changes in temperature. Take the simple case of a moving diaphragm in air: When it moves out, it not only compresses the air it, it also raises its temperature. And the raise in temperature and pressure results in the energy moving outward as the air attempts top reach thermodynamic equilibrium with the surrounding air. And when the diaphragm, conversely, moves inward, not only does the pressure drop, but so does the temperature. Now, it's not that the inside of your enclosure is going to heat up to the point of causing serious thermal problems, it's that the pressure AND the temperature in the box is constantly going up and down, (both by quite small amounts, to be sure). Now, if you're box was PERFECTLY sealed, and the walls were PERFECT thermal insulators AND PERFECTLY rigid (such that 100% the acoustic energy generated by your driver went into increasing and decreasing the internal air pressure (and, at the same time, the temperature), the box would follow perfectly the ideal gas relation, which looks like PV = nRT where P is pressure, V is volume, n is the total amount of gas in the box (in conventional speak, that'd be in mols), R is a nice constant (Boltsmann's in this case) and T is temperature. Any chink in that "perfect" enclosure (a leak, the walls are thermally conductive or can move), and the equation starts to work differently (R, in this case, starts changing). The idea to the fiberglass (or ANY fibrous tangle of the appropriate properties) is not to insulate, but to change the operating conditions of the system. Our "perfect" enclosure would operating under "adiabatic" conditions (constant energy). Pick the right kind of fibrous tangle (and fiberglas, for the restricted purposes of this explanation, is not the ideal stuff), and what happens is that it shifts the oepration to "isothermal" (constant temperature). Behind the big words is a pretty simple principle: with a fibrous tangle in place, when the pressure in the system increases, so does the temeprature, but a portion of that heat is transfered to the tangle. The resulting loss of temeprature results in a reduction in pressure. By the same token, when the pressure is reduced, so is the temeprature, but now the tangle, being every so slightly warmer than the auir, gives up some of its heat, which raises the air temeprature and pressure slightly. Now, the result is that because the presence of the tangle is modifying the thermal and thus the pressure conditions: when you compress it, the pressure doesn go so high, for example, the entire system behaves as if the enclosed volume was slightly larger. Assuming a "perfect" fibrous tangle" (with an appropriate heat capacity and surface area, neither of which fiberglas has), it's theoretically possible to make the enclosure appear about 1.4 times bigger than it really is. Now, put a thermometer inside your enclosure BEFORE you put the stuffing in. Play it REALLY loud for, oh, a day. Come back and look at the temperature. Now, put whatever stuffing you want inside the enclosure and put the thermometer in again, and play the SAME music just as loud for the same time. Then look at the thermometer. (and, to be simple, assume a sealed enclosure in both cases). Can you guess what the difference is going to be (assuming room temperature is the same)? (hint: there will be little if any difference at all). If it's necessary fine, but if not then why bother. I thought the main reason for damping material was to help absorb vibration and keep resonance down. Yes, that's another good reason to have it. The reason why it may NOT be appropriate for a reflex enclosure is because it DOES change the effective volume. Now, assuming your numbers are reasonably accurate, a 143 L enclosure with an inside diameter of 19.25" will have to have an internal length of 30", exclusive of the volume taken up by the woofer and the port. Assuming a perfect absorber, the actual physical length could be about 1.4 times smaller than this, or only 12 inches. Now, whether or not you actually use any absorbtive material is dependent upon a number of things, most of which have to do with the target alignment of system. A so-called Extended Bass Shelf alignment (what I assume you mean by EBS) while it has some bandwidth advantages, but the actual response can be sensitive to tuning parameters (not that you or anyone might case). The actual amount of internal stuffing really depends upon the exact parameters of the woofer usedm the desired response and the acceptable tolerance to misalignment. Certainly, systems such as B4 alignments would really like to have minimal enclosure losses: that not only includes absorbtive losses, but leakage losses as well. At very low frequencies, a small ampount of stuffing is unlikely to make a large difference. But you're not only building a subwoofer with that tube, you're building an organ pipe. And, at 30" long, it's going to support some NASTY 1/2 wave resonances, like a big one at justr above 200 Hz. And don't believe for a moment that your crossover is going to help unless you have yourself a nice, sharp high-order low-pass. Assume you cutoff is 80 Hz and 2nd order: by 200 Hz, your drive to the woofer is down a measely 18 dB at the point where you're near the peak in typical music energy spectrum. Cylindrical enclosure may look neat and be easy to build and may make you feel like it has all sorts of advantages because of its symmetry: but that symmetry makes for very high-Q, sharp line resonances: the worst, by the way, is a spherical enclosure. One might argue that it is or is not mechanically the best, but acoustically, it's a "perfect" disaster. Lot/s of absorbtive ,aterial at one end will help. And I'd line at least half the circumference to try and tame the higher frequency cylinder-mode resonances, if possible. -- +--------------------------------+ + Dick Pierce | + Professional Audio Development | +--------------------------------+ |
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