Any links to where this was originally posted? Not seeing anything using Google search on the Klipsch forum. Thanks.
I now know what caused me the problems.. the two diagrams (1st and 2nd as mentioned previously) in relation to each other specifically when referencing the "double circle". As it (almost certainly) turns-out, all the 2d diagrams are COMPOUND parts - an "assembly" without reference to two parts. This explains why the outer concentric "circle" is presented in diagram. (..I do this myself to often check what the final design looks like 2d, and without removing the "artifact" of the junction between the two (or more) assemblies.) ..of course it doesn't help that the junction circle along with the 2nd diagram's profile appears to be a larger hole "throat" entrance, nor does it help that the directivity is showing a flare at 15 kHz.. which brings me to Paul's measurements here:
The Raptor ... a 10" MTM
-one of the more interesting things with this horn is the transition to midbass on the low-end: where moving down to 700 Hz provided the best dispersion pattern.
Additionally, there is the artifact (notch/dip) at 15 kHz that I would normally associate with a gap between compression driver and the horn's coupling (..ie. a very slight void that is necessarily diffractive).. the thing is though that the VERY excellent ND1460A that is used with this horn has foam coupling ring that should effectively eliminate this problem.
Anyway, it's a very nice design that deserves more attention. ..and it could be made far less costly with a midbass driver substitution (and cabinet volume alteration), particularly with the Scan Speak 26W/8534G00:
26W/8534G00
Here is HiFiCompass's measurement of the 4 ohm version:
ScanSpeak 26W/4534G00 | HiFiCompass
The Raptor ... a 10" MTM
-one of the more interesting things with this horn is the transition to midbass on the low-end: where moving down to 700 Hz provided the best dispersion pattern.
Additionally, there is the artifact (notch/dip) at 15 kHz that I would normally associate with a gap between compression driver and the horn's coupling (..ie. a very slight void that is necessarily diffractive).. the thing is though that the VERY excellent ND1460A that is used with this horn has foam coupling ring that should effectively eliminate this problem.
Anyway, it's a very nice design that deserves more attention. ..and it could be made far less costly with a midbass driver substitution (and cabinet volume alteration), particularly with the Scan Speak 26W/8534G00:
26W/8534G00
Here is HiFiCompass's measurement of the 4 ohm version:
ScanSpeak 26W/4534G00 | HiFiCompass
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Not sure about the original thread, but they are mentioned here:
K-402 in wood! - Page 6 - Technical/Modifications - The Klipsch Audio Community
I still don't see how this follows from the maths. I have reread "Audio Transducers" and now better understand the unusual way the eigenfunctions must fit the boundary conditions. It does seem to be unique to this problem so probably no help from book solutions. But I did find solution software that does not require Mathematica and the associated cost. It uses Matlab but GNU Octave is open source, free and should work. Link is at Ross Adelman, under Software, and also includes a nice paper on the subject. When I reread your book I noticed the picture on p. 76 appears to have a typo, surely the text label should be N not M?
You have a defense, that is a badly drawn illustration where the two outer parts look like projections but, bizarrely, the middle one is not. That would fail even school level technical draftsmanship.
Best wishes David
Hi Dave
First, yes, the drawing is not what one who is versed in engineering drawings would expect. Normally drawings that I see are part drawings to be used to specify the parts for fabrication. It is clear that the drawings that were shown are specifically done to hide the actual interior shape of the device. No one could actually make a part from those drawings, which I did not expect.
As to the polar response, I think that I said before that we know that at high ka values (where here a is the mouth radius) a spherical cap on a sphere will radiate almost uniformly straight ahead. Hence a cap of 45 degrees will yield a directivity of 45 degrees. Thus, if the radial velocity in the mouth of an OS waveguide is approximately uniform then it will radiate out to 45 degrees at HF regardless of the frequency.
The solution of an OS waveguide (see figure 6-10 in my book) shows that the amplitude of the wave at the mouth varies only a small amount at values of C < 10. Above C = 10 I would expect the mouth velocity to begin to have strong focus towards the center of the mouth and hence a narrowing of directivity. But a value of c = 10 means that there have to be about 10-20 wavelengths across the throat for this to happen. That is a very high frequency when compared to what a free disk would see, i.e. a value of ka (where a here is the radius of the disk) of something like 20. At ka = 20 the disk is beaming straight ahead and the OS waveguide is just starting to narrow - a huge difference in the polar responses for the two different situations.
I did not come by this explanation until I had discovered by actual measurements that the polar response of a 1" OS waveguide is wider than that of a 1" disk. I found it out as a way to explain to myself why this was happening. It's real, it does happen, as a look at any of my data will show. Only above about 10 kHz does the DI begin to climb at all and then slowly. It stays flat right up until that point. A 1" piston has a much higher DI at 10 kHz.
What is very true is that for this to happen one must stick very close to the ideal OS contour all the way from the diaphragm to the mouth. Small variations can have very large effects at higher values of C. At a value of C = 10, the variations in the wavefront found at the throat (due to the phase plug) probably dwarf the effect of the directivity narrowing as a result of the OS contour.
So, yes the OS waveguide does narrow at HFs, but not nearly to the extent that a free disk does. Hence the waveguide pulls out the polar response of the disk.
First, yes, the drawing is not what one who is versed in engineering drawings would expect. Normally drawings that I see are part drawings to be used to specify the parts for fabrication. It is clear that the drawings that were shown are specifically done to hide the actual interior shape of the device. No one could actually make a part from those drawings, which I did not expect.
As to the polar response, I think that I said before that we know that at high ka values (where here a is the mouth radius) a spherical cap on a sphere will radiate almost uniformly straight ahead. Hence a cap of 45 degrees will yield a directivity of 45 degrees. Thus, if the radial velocity in the mouth of an OS waveguide is approximately uniform then it will radiate out to 45 degrees at HF regardless of the frequency.
The solution of an OS waveguide (see figure 6-10 in my book) shows that the amplitude of the wave at the mouth varies only a small amount at values of C < 10. Above C = 10 I would expect the mouth velocity to begin to have strong focus towards the center of the mouth and hence a narrowing of directivity. But a value of c = 10 means that there have to be about 10-20 wavelengths across the throat for this to happen. That is a very high frequency when compared to what a free disk would see, i.e. a value of ka (where a here is the radius of the disk) of something like 20. At ka = 20 the disk is beaming straight ahead and the OS waveguide is just starting to narrow - a huge difference in the polar responses for the two different situations.
I did not come by this explanation until I had discovered by actual measurements that the polar response of a 1" OS waveguide is wider than that of a 1" disk. I found it out as a way to explain to myself why this was happening. It's real, it does happen, as a look at any of my data will show. Only above about 10 kHz does the DI begin to climb at all and then slowly. It stays flat right up until that point. A 1" piston has a much higher DI at 10 kHz.
What is very true is that for this to happen one must stick very close to the ideal OS contour all the way from the diaphragm to the mouth. Small variations can have very large effects at higher values of C. At a value of C = 10, the variations in the wavefront found at the throat (due to the phase plug) probably dwarf the effect of the directivity narrowing as a result of the OS contour.
So, yes the OS waveguide does narrow at HFs, but not nearly to the extent that a free disk does. Hence the waveguide pulls out the polar response of the disk.
I plan to just look at the asymptotic solution inside an "infinite" horn.
Practically equivalent but more clear cut, to my mind anyway.
I finally start to have an idea but before I mention it I need to clarify a few questions.
On p. 137 you define "c = kd where d is the inter-focal separation distance"
Isn't d actually half the inter-focal separation distance, as drawn on p. 6?
Isn't k in radians?
So c = 10 is only ~1.5 waves?
Finally, on p.144 the axis label of illustration 6.10 says it's normalized but the value for c=1 is less than 1 for all θ.
How is that?
Best wishes
David
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Earl G, what would you charge for a horn made from stained glass? Would it be possible to get the transitions smooth enough not to matter, or could the transitions make an integral function of the horn? Just saw your "Glass" part on your site, beautiful lamps, but all I could think of was that they would all make really nice looking horns!
Probably a bit expensive for me, but it is a serious question.
Edit:
Maybe it would be possible to make a stained glass horn and smooth the inside with clear epoxy? And maybe add some light diodes to glow slowly at interval in random patterns for more "life" in the beautiful work of art.
Edit2:
How much for a pair of horns for my Radian 475PB?
Probably a bit expensive for me, but it is a serious question.
Edit:
Maybe it would be possible to make a stained glass horn and smooth the inside with clear epoxy? And maybe add some light diodes to glow slowly at interval in random patterns for more "life" in the beautiful work of art.
Edit2:
How much for a pair of horns for my Radian 475PB?
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Dave
Actually the figure on pg. 6 is wrong, pg. 137 is correct. Sorry about that error.
c = kd, but d = 2 a / sin(theta) so k = c sin(theta) / (2 a). Recall that k is the number of wavelengths per unit length so if c=10 then k is about 3.5 / a so k is about 7 wavelengths across the throat. Not 10-20, but still very high since if the throat is .5 in. radius then k = 7 wavelengths / inch which is a very high frequency.
Assuming an infinite waveguide makes the calculations much easier, but not very accurate for directivity unless the frequency is much greater than ka of the mouth. below this frequency the mouth will be a significant factor getting greater as ka falls. At ka = .1 the mouth will dominate the directivity. This is why even a waveguide narrows at mid frequencies, just like any horn does, because the mouth diffraction dominates the directivity.
I would guess that the figure 6-10 was normalized to be unity at C=0.
KaffiMann
A shade needs to only carry its own weight, but a waveguide needs to carry the weight of the driver. Hence stain glass alone would not work because the joints are too weak, one would have to back up the glass construction with a casting of some sort to support the driver weight. The casting could be clear and lit from behind, but it would have to be there.
At this point I have so many projects in the wings that I couldn't even consider doing this, although it would be quite doable. The shape and the lead lines would be fine, but of course you would not want to use a foam insert, which is no small factor in the sound quality of my designs.
Actually the figure on pg. 6 is wrong, pg. 137 is correct. Sorry about that error.
c = kd, but d = 2 a / sin(theta) so k = c sin(theta) / (2 a). Recall that k is the number of wavelengths per unit length so if c=10 then k is about 3.5 / a so k is about 7 wavelengths across the throat. Not 10-20, but still very high since if the throat is .5 in. radius then k = 7 wavelengths / inch which is a very high frequency.
Assuming an infinite waveguide makes the calculations much easier, but not very accurate for directivity unless the frequency is much greater than ka of the mouth. below this frequency the mouth will be a significant factor getting greater as ka falls. At ka = .1 the mouth will dominate the directivity. This is why even a waveguide narrows at mid frequencies, just like any horn does, because the mouth diffraction dominates the directivity.
I would guess that the figure 6-10 was normalized to be unity at C=0.
KaffiMann
A shade needs to only carry its own weight, but a waveguide needs to carry the weight of the driver. Hence stain glass alone would not work because the joints are too weak, one would have to back up the glass construction with a casting of some sort to support the driver weight. The casting could be clear and lit from behind, but it would have to be there.
At this point I have so many projects in the wings that I couldn't even consider doing this, although it would be quite doable. The shape and the lead lines would be fine, but of course you would not want to use a foam insert, which is no small factor in the sound quality of my designs.
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This is the key - on p. 42, equation (3.1.1) you separate the Wave Eqn into the spatial and temporal components. ω is the radian frequency. Then, after (3.1.3) you define the k = ω/c. So k is radians/unit distance, the radian spatial frequency. Do I misunderstand or is there a redefinition I missed?
Yes, I understand mouth effects will matter in a practical horn but I want to do one step at a time, first see the idealized directivity, then consider the mouth. The "infinite" assumption should actually be reasonable for our current discussion because the mooted "pull-out" will matter most at hi frequencies. There are other mouth size issues that I would like to discuss, if you are still interested.
Best wishes David
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It's all correct.
k=w/c=2 Pi / lambda
So if there are 7 wavelength per inch then the frequency at which this occurs is
w/c = 7 radians / inch = 2 Pi f / (12 * 1100 in/sec ) so
f= 7 * 12 * 1100 / 2 / Pi = 14706 Hz, which is a very high frequency, as stated.
So above 14 kHz a waveguide will begin to beam if the phase plug is ideal. However, a 1 inch piston will begin to beam at about ka = 1 or w/c * a = 1, namely
f = 1100 * 12 / 2 / Pi = 1200 Hz
A vast difference in when each device begins to beam.
k=w/c=2 Pi / lambda
So if there are 7 wavelength per inch then the frequency at which this occurs is
w/c = 7 radians / inch = 2 Pi f / (12 * 1100 in/sec ) so
f= 7 * 12 * 1100 / 2 / Pi = 14706 Hz, which is a very high frequency, as stated.
So above 14 kHz a waveguide will begin to beam if the phase plug is ideal. However, a 1 inch piston will begin to beam at about ka = 1 or w/c * a = 1, namely
f = 1100 * 12 / 2 / Pi = 1200 Hz
A vast difference in when each device begins to beam.
I know this is late... I'm just meandering through the thread with nothing of benefit to add.
That said, I thought that the adapter was designed but, Roy never actually tested it so there's no definitive answer to its performance???
I certainly might have missed those conversations but I always kept my eye out for them because I was intrigued about them.
As I recall, Roy said the TAD beams a bit at higher frequencies because of the tunnel of the adapter. The conversation as I recall was, what if you scooted the driver closer to the mouth so as to minimize the length/depth of the tunnel.
Rigma designed it (I'll attach if it will work) and Rigma said he didn't really care for it as he lost some HF content.
My take on that was, he lost some HF content because the sound was now spread out verses beamed and perhaps another PEQ might have fixed it (???)
This is correct. Since a Compression driver puts out a basically falling power response, unless it beams more and more at HFs the response will have to fall. If the polar response is truly CD then the response must fall at 6 dB/oct.
Hello,
We are back from a week at the beach without cable.
I reread the GedLee article on controlled directivity. It is more about controlling early reflections in small listening rooms to build a sound stage. The speakers have a solid toe-in, crossing well in front of the listening position. This toe-in has a much improved sound stage with the early reflections from the right speaker finding their way to the left ear and vice versa.
I still like a large dome midrange over a huge wave guide. The 10 inch midrange that I am using has a Directivity Index of very near 8dB at 2K. The FaitlPro LTH102 waveguide with HF111 CD has a matching DI at the same 2K crossover frequency. The combined mid to CD/Waveguide DI has a gentle controlled uniform slope from 400H (crossover) to 20K.
Thank You DT
We are back from a week at the beach without cable.
I reread the GedLee article on controlled directivity. It is more about controlling early reflections in small listening rooms to build a sound stage. The speakers have a solid toe-in, crossing well in front of the listening position. This toe-in has a much improved sound stage with the early reflections from the right speaker finding their way to the left ear and vice versa.
I still like a large dome midrange over a huge wave guide. The 10 inch midrange that I am using has a Directivity Index of very near 8dB at 2K. The FaitlPro LTH102 waveguide with HF111 CD has a matching DI at the same 2K crossover frequency. The combined mid to CD/Waveguide DI has a gentle controlled uniform slope from 400H (crossover) to 20K.
Thank You DT
This doesn't look correct. I assume you mean 1100 * 12 / 2Pi = 2100 Hz But ka is calculated from the radius, not the diameter. So the value doubles to 4,200 Hz. Of course, it's debatable exactly where to say it starts to beam. A ka of 2 or more looks more realistic to me in the context of a 30° horn. (Subject of a further discussion). But it would double the frequency once more.
Best wishes David
Hi Dave
I agree with your first error of 2.0, the second is questionable.
Let's recall that I posted the fact that measurements of a waveguide show that it has a directivity that is wider than that of a piston source the same size as the throat. You commented that you didn't see how the math predicted that. Clearly the math is different between the two cases of a waveguide and a baffled piston and that it is apparent that the waveguide tends to predict a wider directivity than the baffled piston. This will of course vary with the waveguide angle and will actually go away as the waveguide gets wider and wider.
Some time in the past, probably on the "Geddes on Waveguides" threads, I showed how this effect is probably optimum at 45 degrees (a 90 degree waveguide.) It will likely diminish for narrower and wider devices.
I agree with your first error of 2.0, the second is questionable.
Let's recall that I posted the fact that measurements of a waveguide show that it has a directivity that is wider than that of a piston source the same size as the throat. You commented that you didn't see how the math predicted that. Clearly the math is different between the two cases of a waveguide and a baffled piston and that it is apparent that the waveguide tends to predict a wider directivity than the baffled piston. This will of course vary with the waveguide angle and will actually go away as the waveguide gets wider and wider.
Some time in the past, probably on the "Geddes on Waveguides" threads, I showed how this effect is probably optimum at 45 degrees (a 90 degree waveguide.) It will likely diminish for narrower and wider devices.
Hi Earl
Why questionable? I was worried not to make a slip, always easy to switch a radius with a diameter, or similar error, so I did check it.
Yes, wider directivity may be caused by a source that is not planar, and therefore not equivalent to a piston. My suspicion is that non-planar source may explain some, possibly all, of the wider directivity you have measured. A phase plug can create a "domed" source if the paths are not equalized. Indeed, phase plugs I have seen look as if they would do this, hence my suspicion. So I want to clarify the maths. For the oblate spheroidal co-ordinates you have theta for the co-lattitude, 0 down the horn axis (this makes sense to me, dunno why Mathematica uses lattitude). Then you have parameterized η as cos (theta), it seems. What is ξ exactly?
Best wishes David
So you still don't see how the math predicts a wider response?
The first test that I ever did with an OS waveguide was back in the early 90's. In that test we used a Panasonic 1" flat honeycomb piston tweeter - no phase plug. A perfectly flat source. The polar response was pulled out.
Phase plugs are designed to have a flat source at their outlet so I doubt that your explanation of the phase plug as being the issue is correct. A non-flat throat source will generate more HOMs, all of which have a narrower directivity than the lowest order mode. So the widest directivity will come from a flat source, not a curved one.
ξ is the modified radial dimension equal to the sum of the distances to each foci divided by d the foci separation. On axis it will just be the distance down the device.
The first test that I ever did with an OS waveguide was back in the early 90's. In that test we used a Panasonic 1" flat honeycomb piston tweeter - no phase plug. A perfectly flat source. The polar response was pulled out.
Phase plugs are designed to have a flat source at their outlet so I doubt that your explanation of the phase plug as being the issue is correct. A non-flat throat source will generate more HOMs, all of which have a narrower directivity than the lowest order mode. So the widest directivity will come from a flat source, not a curved one.
ξ is the modified radial dimension equal to the sum of the distances to each foci divided by d the foci separation. On axis it will just be the distance down the device.
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Hello,
This is what I did. I looked and found polar data for the 10 inch JBL 2123 mid-range. I went to the FatialPro site and down loaded their polar data for LTH102 waveguide plus the HF111 driver. The crossover to the woofer, JBL2204 12 inch at 300Hz is down into the room modes. The woofer will be replaced with a JBL2235 15 inch.
I plotted the DI data to graph paper and picked a crossover point (2K) close to the point that the DI curves crossed. All this data stuff is attached.
Further related musings:
I have received from Santa; APx1701 and calibrated microphone, however this stuff is packed for the trip for the trip to the new digs on the California north coast. Real measurements by me after the New Year.
I am doing this for fun and not with the thought this will be the best ever. I have several speakers, compression drivers and horn/waveguides to tryout and test.
Anyone with experience fabricating a Lazy Susan type speaker turntable for off axis frequency response measurements?
Thank You DT
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