http://ldsg.snippets.org/HORNS/ubaffle.html
I recently built an H and U-baffle to investigate sensitivity and polar pattern diff's between the two. To sum up, I saw no LF sensitivity difference between the two and no cardioid polar pattern from the U at LF - rather a dipole pattern. Results are on my webpage.
I recently built an H and U-baffle to investigate sensitivity and polar pattern diff's between the two. To sum up, I saw no LF sensitivity difference between the two and no cardioid polar pattern from the U at LF - rather a dipole pattern. Results are on my webpage.
John,
Thanks for sharing those results. The greatest benefit for me is that the U shape retains a dipole like dispersion. That means that you can get the same results as an H baffle for bass in a much smaller size because the front half of an H baffle is just wasted wood since it adds 0 extra distance for the rear wave to travel.
If you put any more effort into this type of testing, try the same cabs with a driver that goes much lower and has a higher Qts. I believe that will show a significant difference in low end SPL. Using an identical depth cab, the U baffle gives you double the added distance for the rear wave to travel vs an H baffle. To me, that's what results in the claimed 6db SPL advantage down low for the U baffle.
Thanks for sharing those results. The greatest benefit for me is that the U shape retains a dipole like dispersion. That means that you can get the same results as an H baffle for bass in a much smaller size because the front half of an H baffle is just wasted wood since it adds 0 extra distance for the rear wave to travel.
If you put any more effort into this type of testing, try the same cabs with a driver that goes much lower and has a higher Qts. I believe that will show a significant difference in low end SPL. Using an identical depth cab, the U baffle gives you double the added distance for the rear wave to travel vs an H baffle. To me, that's what results in the claimed 6db SPL advantage down low for the U baffle.
Sorry, I don't get your point... The WR125 has a Qts of 0.64, but that doesn't effect anything I was trying to show, afaik. My idea was not to get low bass or any specific response curve out of this enclosure - it was only a test box. I will never listen to it - it will get thrown out.
The point was to see if the shape of the baffle influences the on-axis sensitivity or the polar pattern. The result was that it did not (at least not in the way others have suggested). What I am saying is that the U-baffle cannot be more compact to get the same bass extension as an H-baffle. From my FEA, the H-baffle front chamber is not 'wasted space', as it appears to influence the directional pattern in a positive way, if designed correctly. Also, at low frequencies (below the 1/4 wave resonance of the baffle), the apparent source location moves to the end of the opening of the baffle, so the distance between the front and rear radiation is the same for both an H and U-baffle at low frequencies. This is because all the air contained in the baffle moves as a slug at these frequencies. There is no propagation time for the wave to move a distance down the enclosed path. I have actually measured this before with a probe microphone recording sine pulses at various points in a long line. What you see at high frequencies is that at farther distances from the speaker, it takes some time for the pressure to change because the wave is moving through the air at the speed of sound. At frequencies below the 1/4 wave resonance of the enclosure, the pressure changes everywhere in the enclosure at the same time because all the air is moving together.
The point was to see if the shape of the baffle influences the on-axis sensitivity or the polar pattern. The result was that it did not (at least not in the way others have suggested). What I am saying is that the U-baffle cannot be more compact to get the same bass extension as an H-baffle. From my FEA, the H-baffle front chamber is not 'wasted space', as it appears to influence the directional pattern in a positive way, if designed correctly. Also, at low frequencies (below the 1/4 wave resonance of the baffle), the apparent source location moves to the end of the opening of the baffle, so the distance between the front and rear radiation is the same for both an H and U-baffle at low frequencies. This is because all the air contained in the baffle moves as a slug at these frequencies. There is no propagation time for the wave to move a distance down the enclosed path. I have actually measured this before with a probe microphone recording sine pulses at various points in a long line. What you see at high frequencies is that at farther distances from the speaker, it takes some time for the pressure to change because the wave is moving through the air at the speed of sound. At frequencies below the 1/4 wave resonance of the enclosure, the pressure changes everywhere in the enclosure at the same time because all the air is moving together.
John,
Thanks for that slug of air explanation and the front end of the H baffle being the source. Now I understand that the driver isn't responsible for the results. Would a more typically dimensioned H baffle still act in the same manner?
Wouldn't the results of a W baffle woofer alignment contradict this, since it seems that the rear wave / front wave distance differential ("d") is much greater than just the depth of the W baffle cab?
Also, I use folded back "wings" on my OB's which aren't anywhere near 90 degrees from the front baffle. Is this resulting in a similar phenomenon in that cavity and the source of my rear wave is not at the driver?
Thanks for that slug of air explanation and the front end of the H baffle being the source. Now I understand that the driver isn't responsible for the results. Would a more typically dimensioned H baffle still act in the same manner?
Wouldn't the results of a W baffle woofer alignment contradict this, since it seems that the rear wave / front wave distance differential ("d") is much greater than just the depth of the W baffle cab?
Also, I use folded back "wings" on my OB's which aren't anywhere near 90 degrees from the front baffle. Is this resulting in a similar phenomenon in that cavity and the source of my rear wave is not at the driver?
On the W-baffle, I'm not sure... Can you point me towards some results? I could not find any. I think the seperation distance would just be the length of the cabinet, same as for the H and U, at least at low frequencies.
One other thing to point out is that Linkwitz (and probably others) assume that the baffle depth is large compared to the cross section. This is clearly NOT the case in what I've built and measured. Then again, it is not necessarily the case in common U and H baffles either. Consider a 24 inch long U baffle for a 12" woofer - it's probably going to be something like 13" or 14" in width internally. My test boxes are a bit further away from the theoretical case than that - they're 8 inches wide and 12 inches long, so it would make some sense that they do not do exactly what is predicted by some of the theory on Linkwitz's site, for example.
One other thing to point out is that Linkwitz (and probably others) assume that the baffle depth is large compared to the cross section. This is clearly NOT the case in what I've built and measured. Then again, it is not necessarily the case in common U and H baffles either. Consider a 24 inch long U baffle for a 12" woofer - it's probably going to be something like 13" or 14" in width internally. My test boxes are a bit further away from the theoretical case than that - they're 8 inches wide and 12 inches long, so it would make some sense that they do not do exactly what is predicted by some of the theory on Linkwitz's site, for example.
John,
I've got to say that you are being a pioneer with your real world measurements with dipoles and I applaude your efforts. While SL provides a wealth of info and theory, he shows us how to get flat results using electronics. Many of us want to know how to get great results without the EQ and lots of electronics, but instead to use baffle construction. I wish I was close to you geographically. I'd do the construction and bring stuff to you for measurement and really get to the bottom of what is optimum.
If what you are saying is true and I believe it is, then my way of thinking about how folded baffles work is out the window. For example, I have a W baffle woofer with 2 12 inch drivers which is only 19" deep and it has good bass down into the 40's. Your test results tell me that I'm getting good bass more because of dispersion than the difference in travel distance for the front and back waves. It seems that the folded baffle creates a wave guide so most of the back wave energy travels back and front wave energy forward instead of both propagating in a sphere like bass from a boxed speaker. Am I on the right track?
I've got to say that you are being a pioneer with your real world measurements with dipoles and I applaude your efforts. While SL provides a wealth of info and theory, he shows us how to get flat results using electronics. Many of us want to know how to get great results without the EQ and lots of electronics, but instead to use baffle construction. I wish I was close to you geographically. I'd do the construction and bring stuff to you for measurement and really get to the bottom of what is optimum.
If what you are saying is true and I believe it is, then my way of thinking about how folded baffles work is out the window. For example, I have a W baffle woofer with 2 12 inch drivers which is only 19" deep and it has good bass down into the 40's. Your test results tell me that I'm getting good bass more because of dispersion than the difference in travel distance for the front and back waves. It seems that the folded baffle creates a wave guide so most of the back wave energy travels back and front wave energy forward instead of both propagating in a sphere like bass from a boxed speaker. Am I on the right track?
Thanks, but I would like to say that Linkwitz's site is really a great resource, imo. He does more or less show you how to design a dipole speaker (actually he shows you exactly with his Phoenix and Orion projects). But if you want to do something different, you just have to take his information to figure out a starting point and then start building and measuring. If you can't measure the results of what you build, then you're just shooting in the dark. Even my FEA stuff is not a replacement for building and measuring a speaker - with more refinement it could do more (simulate cone breakup, etc.), but at some point it is easier and faster to just build something. If you have some theoretical background such as Linkwitz provides, then you are better set to interpret the results of the measurements of your experiment and improve on it quickly. This is basically what SL says he does:
http://www.linkwitzlab.com/faq.htm#Q24
Also, looking at Linkwitz's dipole information, I don't think anything I've done really contradicts his information - just expands on it with one specific example. He shows models for an H-baffle that clearly give the distance of seperation as the outside length of the cabinet. The W-baffle is just a more compact way to package more woofers into the same cabinet size (so more volume displacement).
I would also say that at the frequencies we are interested in and the size of the baffles, there is no waveguide effect - the sound waves do propagate spherically from the ends of the enclosure. To influence the polar pattern at low frequencies besides through cancellation, you need very large waveguides, like roughly 20 feet wide to confine the pattern to 90 degrees, for example.
http://www.linkwitzlab.com/faq.htm#Q24
Also, looking at Linkwitz's dipole information, I don't think anything I've done really contradicts his information - just expands on it with one specific example. He shows models for an H-baffle that clearly give the distance of seperation as the outside length of the cabinet. The W-baffle is just a more compact way to package more woofers into the same cabinet size (so more volume displacement).
I would also say that at the frequencies we are interested in and the size of the baffles, there is no waveguide effect - the sound waves do propagate spherically from the ends of the enclosure. To influence the polar pattern at low frequencies besides through cancellation, you need very large waveguides, like roughly 20 feet wide to confine the pattern to 90 degrees, for example.
John,
I am glad to see others looking at U and H frame woofer systems but I would like to make a couple of points re your measurement and calculations. First, you calculations look very nice and are probably a reasonable representaion of the behavior of an undamped U-frame. They are not unlike those which will be obtained from the MathCAD spread sheet delevoped by Martin King and myself (mostly Martin's work with some direction by me). However, as you are aware, damping is crucial to the perfromance of the U-frame system. Martin's and my work sheet include a suitable damping model.
The next issue is your attempts to measure the system response. Unfortunately it really isn't possibble to get an accurate picture of what the on axis or polar response is by making measurements as you have. The problem is that the measurement must be done in the far field as they are dependent on the distances from the front and rear sources. For example, regradless of the length of the H or U-frame, as you approach the front source you end up basically with a measurement of the SPL radiated by that source and, aside for the possible differences in the enclosure associated resonances, this will basically be the drivers near filed response. In your case where you measured at 0.5m the front SPL would be nominally higher than the rear by at least 4.1dB due to simple path length differences. This applies to H dipole, U-frames and ture, 2 source cardiods. What I am saying here with regard to a true 2-source cardiod is when you have two monopoles seperated by some distance D with one system phase inverted and delayed by D/C (c= sound speed). This is a ture cardioid but if you measure it from .5m directly behind the system there won't be a null due to the SPL amplitude differences. It is necessary to get out into the far field to see the null behavior.
Anyway, this morning I put together a web page showing how the performance of U and H frames can be more accurately evaluated using near filed measurements. It can be viewed here
http://www.geocities.com/kreskovs/DIY-dipole.html
Be patient. I suffer from data transfer limitations and you may not be able to view the content imediately.
I am glad to see others looking at U and H frame woofer systems but I would like to make a couple of points re your measurement and calculations. First, you calculations look very nice and are probably a reasonable representaion of the behavior of an undamped U-frame. They are not unlike those which will be obtained from the MathCAD spread sheet delevoped by Martin King and myself (mostly Martin's work with some direction by me). However, as you are aware, damping is crucial to the perfromance of the U-frame system. Martin's and my work sheet include a suitable damping model.
The next issue is your attempts to measure the system response. Unfortunately it really isn't possibble to get an accurate picture of what the on axis or polar response is by making measurements as you have. The problem is that the measurement must be done in the far field as they are dependent on the distances from the front and rear sources. For example, regradless of the length of the H or U-frame, as you approach the front source you end up basically with a measurement of the SPL radiated by that source and, aside for the possible differences in the enclosure associated resonances, this will basically be the drivers near filed response. In your case where you measured at 0.5m the front SPL would be nominally higher than the rear by at least 4.1dB due to simple path length differences. This applies to H dipole, U-frames and ture, 2 source cardiods. What I am saying here with regard to a true 2-source cardiod is when you have two monopoles seperated by some distance D with one system phase inverted and delayed by D/C (c= sound speed). This is a ture cardioid but if you measure it from .5m directly behind the system there won't be a null due to the SPL amplitude differences. It is necessary to get out into the far field to see the null behavior.
Anyway, this morning I put together a web page showing how the performance of U and H frames can be more accurately evaluated using near filed measurements. It can be viewed here
http://www.geocities.com/kreskovs/DIY-dipole.html
Be patient. I suffer from data transfer limitations and you may not be able to view the content imediately.
I always interpreted SL's H baffle example to be that "d" was actually the distance from the back of the baffle to the rear edge plus the rear edge to the front of the baffle which is essentially the depth of the cab. However, what you are saying is that the rear wave does not travel from the cone to the rear edge of the cabinet. It exists the rear cavity instantly. Is that really how it works? If you put a mic inside the cavity is there sound? It just doesn't make sense to me that a 19" distance differential is going to get me results that sound flat down to the low 50's. There must be more at work here.
Hi John (K),
Thanks for pointing out the difference in SPL due to the mic distance - I had not thought of this and it makes my close measurements even worse than I had initially thought. I tried your nearfield method method this morning and did get a cardioid-like response in some cases. It seems to vary significantly with frequency and observation distance though, which makes me wonder about my calculation method (and is why I was trying to avoid this route). Putting in the same SPL for both front and rear radiation but adding 180 degrees of phase to the rear produces a dipole pattern at all frequencies / distances, so this would make me think it is okay... I guess I will have to try far field measurements once I get my mobile system working again and see what happens there.
Also, from my nearfield measurements the damping seems to have a large effect around the resonance of the line, but creates less than 1dB of difference from the unstuffed case at lower frequencies. Is this consistent with what you have seen?
Thanks for pointing out the difference in SPL due to the mic distance - I had not thought of this and it makes my close measurements even worse than I had initially thought. I tried your nearfield method method this morning and did get a cardioid-like response in some cases. It seems to vary significantly with frequency and observation distance though, which makes me wonder about my calculation method (and is why I was trying to avoid this route). Putting in the same SPL for both front and rear radiation but adding 180 degrees of phase to the rear produces a dipole pattern at all frequencies / distances, so this would make me think it is okay... I guess I will have to try far field measurements once I get my mobile system working again and see what happens there.
Also, from my nearfield measurements the damping seems to have a large effect around the resonance of the line, but creates less than 1dB of difference from the unstuffed case at lower frequencies. Is this consistent with what you have seen?
(JPK) I cant see I confused you a bit. Fitst conside the H frame since, being symmetric, it is simpler to visualize. The driver generates an acoustic wave that travels from the driver to the open ends. I don't knwo what SL's terminology is but assume that the length of the H frame is L so that the driver is at L/2. Both the front and back wave reach the opening afer propogating a distance L/2 with associated propogation delay. The front and rear SPL measured in the plane of the openings will be identical in amplitude, front and rear, but inverted in phase. From the opening they propagate into free space. Obviouly, on axis the front wave propagtes directly to the measurement point. However the rear wave must propagate externally an additional distance L, the length of the H frame and will have an additional delay of L/C. Any effect of the delays internal to the H frame are already in the phase response measured at the openings so they need not be considered. Also, they don't effect anything because what ever they are, they are equaly for the front and rear due to the symmetry of an H frame. The H frame is no different than two monopole woofers seperated by a distance L with one out of phase.
You could also look at the H frame using the driver position as a reference. In that case the front wave propagates axially driectly from the driver cone to the listener (looking down the barrel). The rear wave first propagates backwards a distance of L/2 internally and then forwards, externally, another distance of L/2 before it gets to the axial position of the source of the front wave (driver cone). Thus the total delay is L/C. If you look at it from behind the same thing is found. The front wave is delayed by L/C before it gets to the point of origin of the back wave.
The U-frame is different Consider a U-frame that is only L/2 in total lenght. This is like cutting off the front half of the H frame discussed above off. Any internal delays are still contained in the SPL measurements. Again, like the H frame, the front wave propogates directly to the listener and the rear wave propogates L/2 backwards internally and then L/2 forwards, externally, to get the the poisition of the front source; total delay L/C. But from the rear, the front and rear wave propogare from the same point, just different sides of the driver, neglecting the width of the baffle. So from the rear there is not differential delay and the front and rear are just 180 degrees out of phase. So you see from this simple analysis it is readilly apparent that from the front the propagation distances for the front and rear wave for the L/2 length U frame is the same as those for the L length H frame.
The problems come in because of the 1/4 wave resonances. In the undamped case the 1/4 wave resonance gives rise to a negative GD which cancels the internal propagation delay. For an H frame it is of no consequence since it is symmetric; both front and rear have the same effect. However, in a U-frame it effectively cancels the delay associated with the rear internal propagation. If it weren't for the fact that the SPL amplitude response is asymmetric in the U-frame, the undamped U-frame would act like a dipole of length L/2 and at frequencies well below the 1/4 wave resonance it does. Now let's look at the role of the damping in the u-frame. One way which is commonly discussed and is incorrect IMO, is that acoustic resistance is added to the rear chanber and this forms an LP filter with GD that delays the rear response by L/(2C). This is the lumped paramter type approach. That would be fine IF the SPL amplitude were the same front and rear. But they are not. The other way is to look at the real result. As I said, the 1/4 wave resonance introduce a negative GD below resonance. However, if the resonance could be equalized that negative GD would be removed and the propogation delay from the driver to the rear openinf would gain be L/(2C). Equalizing the resonance would also result in symmetric amplitude response for the front and rear with the result that now you would have a true cardioid response from the U frame. This is really the more comprehensice way to look at the u-frame problem. However, as usual there is a caveat. It's just not possible to damp only the resonance. Damping materials generally don't do much at very low frequency and damp more as the frequency rises. Below resonance this is exactly what is wanted. However, above resonance the damping either continues to increase or flatten out. What we would like is a damping material that acts only around the resonant frequency. Since we don'ty have that what we must do is recognize that any damping effectively ddoes two things. 1) equalizes the resoance removingsome of the associated negative GD and 2) creates a low pass filter that attenuates the rear response above resonance more than we would like and also introduces some positive GD as is the case for any LP filter. The problem is then to find the correct amount of damping necessary to restore the correct internal delay of the U-frame and at the same time driving the front and rear amplitude response towards symmetry to as close to the 1/4 wave resonant frequency as possibly. The better this is done the higher the useful cut off frequency of the U-frame woofer system. In the case I have on my web site there is excellent symmerty between front and rear radiation to about 50 or 60 Hz with the correct internal delay. Above 60 Hz the amplitude starts to loose symmetry and the result is evident in the poorer cancelation at 180 degrees. However, since the delay is still close to correct the onaxis response doesn't suffer as much. Obviouly, the null is much more sensitive to these errors than the on axis sum, as would be expected. Remember, the internal delay for the rear SPL radiation is included in the SPL phase measurement taken at the rear opening plane.
Hope this helps. It's a lot to think about.
Happy NEw Year.
You could also look at the H frame using the driver position as a reference. In that case the front wave propagates axially driectly from the driver cone to the listener (looking down the barrel). The rear wave first propagates backwards a distance of L/2 internally and then forwards, externally, another distance of L/2 before it gets to the axial position of the source of the front wave (driver cone). Thus the total delay is L/C. If you look at it from behind the same thing is found. The front wave is delayed by L/C before it gets to the point of origin of the back wave.
The U-frame is different Consider a U-frame that is only L/2 in total lenght. This is like cutting off the front half of the H frame discussed above off. Any internal delays are still contained in the SPL measurements. Again, like the H frame, the front wave propogates directly to the listener and the rear wave propogates L/2 backwards internally and then L/2 forwards, externally, to get the the poisition of the front source; total delay L/C. But from the rear, the front and rear wave propogare from the same point, just different sides of the driver, neglecting the width of the baffle. So from the rear there is not differential delay and the front and rear are just 180 degrees out of phase. So you see from this simple analysis it is readilly apparent that from the front the propagation distances for the front and rear wave for the L/2 length U frame is the same as those for the L length H frame.
The problems come in because of the 1/4 wave resonances. In the undamped case the 1/4 wave resonance gives rise to a negative GD which cancels the internal propagation delay. For an H frame it is of no consequence since it is symmetric; both front and rear have the same effect. However, in a U-frame it effectively cancels the delay associated with the rear internal propagation. If it weren't for the fact that the SPL amplitude response is asymmetric in the U-frame, the undamped U-frame would act like a dipole of length L/2 and at frequencies well below the 1/4 wave resonance it does. Now let's look at the role of the damping in the u-frame. One way which is commonly discussed and is incorrect IMO, is that acoustic resistance is added to the rear chanber and this forms an LP filter with GD that delays the rear response by L/(2C). This is the lumped paramter type approach. That would be fine IF the SPL amplitude were the same front and rear. But they are not. The other way is to look at the real result. As I said, the 1/4 wave resonance introduce a negative GD below resonance. However, if the resonance could be equalized that negative GD would be removed and the propogation delay from the driver to the rear openinf would gain be L/(2C). Equalizing the resonance would also result in symmetric amplitude response for the front and rear with the result that now you would have a true cardioid response from the U frame. This is really the more comprehensice way to look at the u-frame problem. However, as usual there is a caveat. It's just not possible to damp only the resonance. Damping materials generally don't do much at very low frequency and damp more as the frequency rises. Below resonance this is exactly what is wanted. However, above resonance the damping either continues to increase or flatten out. What we would like is a damping material that acts only around the resonant frequency. Since we don'ty have that what we must do is recognize that any damping effectively ddoes two things. 1) equalizes the resoance removingsome of the associated negative GD and 2) creates a low pass filter that attenuates the rear response above resonance more than we would like and also introduces some positive GD as is the case for any LP filter. The problem is then to find the correct amount of damping necessary to restore the correct internal delay of the U-frame and at the same time driving the front and rear amplitude response towards symmetry to as close to the 1/4 wave resonant frequency as possibly. The better this is done the higher the useful cut off frequency of the U-frame woofer system. In the case I have on my web site there is excellent symmerty between front and rear radiation to about 50 or 60 Hz with the correct internal delay. Above 60 Hz the amplitude starts to loose symmetry and the result is evident in the poorer cancelation at 180 degrees. However, since the delay is still close to correct the onaxis response doesn't suffer as much. Obviouly, the null is much more sensitive to these errors than the on axis sum, as would be expected. Remember, the internal delay for the rear SPL radiation is included in the SPL phase measurement taken at the rear opening plane.
Hope this helps. It's a lot to think about.
Happy NEw Year.
John K and John S,
We've got 2 people who really know their stuff saying 2 different things. At low frequencies does the wave propagate down these passages as John K stated or does the air in the passage move as a slug instantly so the source is truely the end of the passage as John S stated.
If it is moving to the end instantly as a slug as John S has measured, wouldn't a larger exit than start cause the wave propagate from the cone for the U baffle like in a horn? This would make its bass extension even better because you would pick up 2L as the path distance differential for the front and rear waves?
We've got 2 people who really know their stuff saying 2 different things. At low frequencies does the wave propagate down these passages as John K stated or does the air in the passage move as a slug instantly so the source is truely the end of the passage as John S stated.
If it is moving to the end instantly as a slug as John S has measured, wouldn't a larger exit than start cause the wave propagate from the cone for the U baffle like in a horn? This would make its bass extension even better because you would pick up 2L as the path distance differential for the front and rear waves?
johninCR said:
(JPK) The reality is that waves always take time to propogate. Treating the air as a slug is a lumped parameter approximation that is often introduced to simplify the problem where appropriate. The justification would go something like this. At low frequency where the wave length is very long compared to the dimensions of the device (U-frame in this case) the variations in pressure along the length of the u-frame are small compared to the variation in pressure over a complete cycle. The lumped parameter analysis is fine if all you want to know is the frequency response at the exit plane of the U-frame. But when it is added to the front response and accurate phase information is required the propogation delay must be accounted for.
The point is that it is necessary to define what the important aspects of the physics are before introducing any assumption about how the problem is to be solved. When summing the front and rear responses the relevant length scales (and delays) are those associated with the dimensions of the u-frame, not the wave lengths of the radiated sound. If you look at "Theory of acoustical resistance enclosures" by Juha Backman you can get an idea of how a lumped paramter analysis can be used with the additional consideration of a delay. This is commonly done in the analysis of TL speaker system and a u-frame is very similar to a TL tuned well above the driver's Fs.
It's all good. Happy New Year
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