The colorful 2D graphs are very detailed pressure maps of the output coming from the two test horns. The reference level is taken at 0 degrees, and is dark red. Yellow is -8 dB down from the zero-axis level, and deep blue is -20 dB down.
The measurements are taken with an automated MLSSA system and an X-Y traverse system to move the microphone across an XY axis in front of the rigidly mounted horn. As you can see from the captions, the microphone is stepped across 300mm in each direction.
If a horn had perfectly uniform dispersion across the desired beamwidth, it would be deep red all the way across. If the beam is much tighter, the deep red region will be confined to a small area in the center. It bears repeating these are NOT simulations, like the ones we see elsewhere on DIYAudio. These are very detailed measurements of the real thing.
The non-axisymmetric High Order Modes (HOMs) that Dr. Geddes and I have been discussing are those weird-looking side lobes, most notably in the 2840 Hz graph (Fig. 3.12). Oddly enough, that's the one picture where the caption appears to be correct, with the conical horn showing the widest dispersion.
The conical does have the widest dispersion in a paint-sprayer sense (as in "coverage"), but there are very unpleasant-looking sidelobes - five of them, in a rough, unsymmetric 5-pointed pattern. Webster horn theory has nothing to say about these asymmetric sidelobes, and the Morgans paper doesn't go beyond computer modeling of axisymmetric lobing patterns. These measured (not predicted) patterns are not the same as axisymmetric lobing.
Note the peak-to-dip magnitudes (between the hotspot and the minima between the sidelobes) is about 3 to 3.5 dB - not huge, but not desirable, and probably audible as well. Since a conventional polar-pattern plot would represent a single, narrow slice through one of these 2D graphs, it probably would not pick up these peaks and minima very well - it really takes a 2D representation to show how serious they really are.
Instead of being random, these sidelobes appear to be chaotic - large, complex systems that are extremely sensitive to initial events. In this case, the probable causes are very small off-center or non-circular horn mounting, phase-plug construction, or diaphragm alignment. As Dr. Geddes mentioned in a previous post, something as simple as rotating the compression driver 90 or 120 degrees causes these non-axisymmetric HOM's to move around. That points to very small errors in the horn mounting, phase-plug construction, or diaphragm alignment.
The measurements are taken with an automated MLSSA system and an X-Y traverse system to move the microphone across an XY axis in front of the rigidly mounted horn. As you can see from the captions, the microphone is stepped across 300mm in each direction.
If a horn had perfectly uniform dispersion across the desired beamwidth, it would be deep red all the way across. If the beam is much tighter, the deep red region will be confined to a small area in the center. It bears repeating these are NOT simulations, like the ones we see elsewhere on DIYAudio. These are very detailed measurements of the real thing.
The non-axisymmetric High Order Modes (HOMs) that Dr. Geddes and I have been discussing are those weird-looking side lobes, most notably in the 2840 Hz graph (Fig. 3.12). Oddly enough, that's the one picture where the caption appears to be correct, with the conical horn showing the widest dispersion.
The conical does have the widest dispersion in a paint-sprayer sense (as in "coverage"), but there are very unpleasant-looking sidelobes - five of them, in a rough, unsymmetric 5-pointed pattern. Webster horn theory has nothing to say about these asymmetric sidelobes, and the Morgans paper doesn't go beyond computer modeling of axisymmetric lobing patterns. These measured (not predicted) patterns are not the same as axisymmetric lobing.
Note the peak-to-dip magnitudes (between the hotspot and the minima between the sidelobes) is about 3 to 3.5 dB - not huge, but not desirable, and probably audible as well. Since a conventional polar-pattern plot would represent a single, narrow slice through one of these 2D graphs, it probably would not pick up these peaks and minima very well - it really takes a 2D representation to show how serious they really are.
Instead of being random, these sidelobes appear to be chaotic - large, complex systems that are extremely sensitive to initial events. In this case, the probable causes are very small off-center or non-circular horn mounting, phase-plug construction, or diaphragm alignment. As Dr. Geddes mentioned in a previous post, something as simple as rotating the compression driver 90 or 120 degrees causes these non-axisymmetric HOM's to move around. That points to very small errors in the horn mounting, phase-plug construction, or diaphragm alignment.
It was my understanding that these were taken at the mouth and not in the far field. Correct? What one really wants is the velocity in the plane of the mouth not the pressure. But if these are at the mouth then a constant color would not yield a constant directvity. It would be hard to interprete these pressure plots since its the normal velocity that creates the far field, but with pressure only what you are looking at is proportional to the velocity magnitude independent of the direction.
The HOM will appear as non-axisymmetric plots, but rings would also be HOMs since the primary wave should be a color changing slowly in the radial direction.
The HOM will appear as non-axisymmetric plots, but rings would also be HOMs since the primary wave should be a color changing slowly in the radial direction.
Considering the total traverse is only 300mm, near-field is seems most likely.
So what are we really looking at? What do the hotspots correspond to in the far field (where we listen)? Do the hotspots correspond to the spikes in the traditional far-field polar plots, or are they different? If it is normal velocity that creates the far-field pressure, that makes interpreting these graphs problematic - although the asymmetric maxima we see in the graphs would not seem to bode well for the far-field.
So what are we really looking at? What do the hotspots correspond to in the far field (where we listen)? Do the hotspots correspond to the spikes in the traditional far-field polar plots, or are they different? If it is normal velocity that creates the far-field pressure, that makes interpreting these graphs problematic - although the asymmetric maxima we see in the graphs would not seem to bode well for the far-field.
Thats the problem, the conversion from a velocity distribution to the far field pressure is a transform, a Bessel transform in this case (circular), identical to that used for optical lens calculations. If the aperature were square then the far field would be the 2-D Fourier transform of the velocity distribution. Hows your ability to imagine that in your head? Basically, just like the normal FFT a narrow pulse is a wide polar, so the ideal would be a Gaussian fall off to the edge - I talk about this in my book and Morgan references that discussion in his thesis. A Gaussian velocity distribution in the mouth will yield a Gaussian polar response - no lobes, just a smooth fall-off.
If these are pressures only then you don't even have enough information to calculate the far-field.
A lot of people are getting this wrong I find these days. A sweep of the pressure field alone cannot predict the far field because the direction of the velocity is missing. You can make some assumption about the velocity - like its normal - and get the far field, but then its only as good as your assumption is correct. For a horn this would be highly erroneous.
If these are pressures only then you don't even have enough information to calculate the far-field.
A lot of people are getting this wrong I find these days. A sweep of the pressure field alone cannot predict the far field because the direction of the velocity is missing. You can make some assumption about the velocity - like its normal - and get the far field, but then its only as good as your assumption is correct. For a horn this would be highly erroneous.
gedlee said:
That makes sense - similar to the FFT transform between time and frequency domains. It's unfortunate we don't have the velocity, nor its vector, for all of those 3000+ points. Does the 2D pressure map tell us anything useful, then, except to draw our attention to potential non-axisymmetric HOM's?
In essence, no there is nothing concrete that we can take-away from this. Its interesting, but doesn't tell us much about what to do or what will happen in the far-field.
The time-frequency relationship becomes the space-wavenumber relationship in radiation problems (physicists will recognize that these two things are equivalent in Quantum Mechanics).
The best that we could do is "assume" that the wavefronts were nearly spherical then we could calculate the normal velocity by assuming the pressures were the velocity magnitudes. From this we could calculate the far field radiated pressure. This would be correct to first order, but would certainly have some second order errors. The "purer" the wavefront - because there were fewer HOMs - like an OS waveguide with foam - the better this would work. For a diffraction type device it would probably not even be correct to first order.
I do have to admit to being a little rusty on Nearfield Acoustic Holography which takes a surface of pressure measurements and propagates it to the far-field, but I forgot what assumptions are made there. I'll have to look that up in "Williams".
The time-frequency relationship becomes the space-wavenumber relationship in radiation problems (physicists will recognize that these two things are equivalent in Quantum Mechanics).
The best that we could do is "assume" that the wavefronts were nearly spherical then we could calculate the normal velocity by assuming the pressures were the velocity magnitudes. From this we could calculate the far field radiated pressure. This would be correct to first order, but would certainly have some second order errors. The "purer" the wavefront - because there were fewer HOMs - like an OS waveguide with foam - the better this would work. For a diffraction type device it would probably not even be correct to first order.
I do have to admit to being a little rusty on Nearfield Acoustic Holography which takes a surface of pressure measurements and propagates it to the far-field, but I forgot what assumptions are made there. I'll have to look that up in "Williams".
When looking at pressure plots like these, one needs to understand that this is a planar section pressure view; however, the wave front it no longer planar. So depending on the wave length, you will see very different dispersion implications that could be misleading. Dr. Geddes may be right about viewing the velocity profile. If we look at pressure, then it would have to be along the shape of the wave front.Lynn Olson said:
Hmmm… Every time I feel like I’m ready to start on constructing an oblate spheroid waveguide I get bewildered from more discussion. This thing keeps on getting more complex with every question. I feel like the more I learn the less satisfied I am with the design. I really want to do this correctly so my results will not be compromised. It is quite frustrating for me. I have a ton of experience designing and constructing axis-symmetric tractrix horns. You could tell me the compression you’re using and your desired low frequency limit, and I can hit the design goal right on the nose. The oblate spheroid on the other hand is an entirety different beast. Should I just go ahead and construct one and see what happens, or continue to put it off? I’m not feeling too confident here. Perhaps, I’m over thinking this, yes/no?
Rgs, JLH
Rgs, JLH
Well, the mesh type coloring tells that FEA is used for at least post processing of measured data. Why do you think not?gedlee said:
Additionally, if measurement is taken at the mouth, due to the wave front shapr, the actual phase would be different, thus implying different location and different pressure in a pressure wave cycle. Is there any reason to believe not so? and why.
I would very much like to hear what you experience, whether the good points or bad points, after constructing these different types of horns/guides. From directivity control, I can see the benefits of different directivity of control patterns. If we consider the nature of instruments in their common locations and the signal nature of those instruments and vocals, I do wonder what balance of controlled directivity would be optimum. But then, we have this horn type resonance which is very common, and which does mask out some detail information in addition to smearing of image. Audio is a really complicated technology, and there are many people whom have spent thier lifetime studying it.JLH said:
Ah, the mesh is used to position the mic! But the transverse system can potentially generate reflections that will effect measurements. I like the length of Lyns's mic much better. Don't see any information on how they align the horn axis with the mesh.soongsc said:
Oh, now I see they are doing a whole frequency spectrum at each mesh and picking the value off from a particular frequency after FFT.
If we do a baffled piston analysis and look at the beam pattern at different frequencies, the main lobe is apprioximately the maximum beam width we can get out of a throat for a specific diameter. Now the question would be controlling the beam at lower frequencies.
JLH said:
If Dr. Geddes says the OS has the lowest possible diffraction and HOMs, I would take him at his word. Diffraction and HOM's (axisymmetric and non-axisymmetric) are the dominant unwanted horn artifacts; not only that, they do not readily respond to equalization, since they are time-domain errors. HOM and diffraction minimization are a very desirable goals in any loudspeaker, regardless of design philosophy.
It would seem a near-certainty the OS will sound different than the Tractrix horns you have already built, so why not go ahead and find out for yourself?