The patent continues:
"Increasing the B1 product causes the peaks in response at the edge of the band (for which the tube length is an odd multiple of a quarter wavelength) to increase similar to the effect of increasing the ATCR. Thus, a low ATCR may be partially offset by using a higher B1 product. Furthermore, a higher B1 product decreases the sensitivity in midband where the length of the longer tube is a half wavelength. Preferably the B1 product is selected to help provide a more uniform response. For a given geometry of cone and tubes B1 is preferably selected such that the response at the frequency corresponding to .lambda./4 of the large tube is comparable to the response at the frequency corresponding to .lambda./2 of the large tube."
Now, I know this much-Bl product is related to Qts. That is to say, all other things being equal, a speaker with a higher Bl product has a lower Qts. Also, Qts is a measure of speaker damping, I believe, with the lower Qts having a higher damping.
To check if your Qts is too low, perhaps you should attach a resistor in series with the woofer. If the response smooths out, then a higher Qts woofer is in order. The response will come down because of the resistor in any event-it is the ratio of peaks to valleys that the higher Qts hopefully will help.
If the response does smooth out, then experiment around with resistors and putting a smaller tube inside the larger tube. You might need a different woofer.
"Increasing the B1 product causes the peaks in response at the edge of the band (for which the tube length is an odd multiple of a quarter wavelength) to increase similar to the effect of increasing the ATCR. Thus, a low ATCR may be partially offset by using a higher B1 product. Furthermore, a higher B1 product decreases the sensitivity in midband where the length of the longer tube is a half wavelength. Preferably the B1 product is selected to help provide a more uniform response. For a given geometry of cone and tubes B1 is preferably selected such that the response at the frequency corresponding to .lambda./4 of the large tube is comparable to the response at the frequency corresponding to .lambda./2 of the large tube."
Now, I know this much-Bl product is related to Qts. That is to say, all other things being equal, a speaker with a higher Bl product has a lower Qts. Also, Qts is a measure of speaker damping, I believe, with the lower Qts having a higher damping.
To check if your Qts is too low, perhaps you should attach a resistor in series with the woofer. If the response smooths out, then a higher Qts woofer is in order. The response will come down because of the resistor in any event-it is the ratio of peaks to valleys that the higher Qts hopefully will help.
If the response does smooth out, then experiment around with resistors and putting a smaller tube inside the larger tube. You might need a different woofer.
This illustration is something that might be used to fit a thinner tube into both sides of the Cannon.
Of course, if worse comes to worse, you can always cut some of the tube off, put a couple of vent holes in it, mount the woofer in front of one end, plug up the back end, and make it a reflex tube sub a la Hsu.
Of course, if worse comes to worse, you can always cut some of the tube off, put a couple of vent holes in it, mount the woofer in front of one end, plug up the back end, and make it a reflex tube sub a la Hsu.
Attachments
Thinking about Drew's configuration with the Peerless XLS and the 18 foot long pipe.
If I understand the patent correctly, a twelve foot pipe would require a speaker with an Fs of 63 Hz.
An 18 foot pipe Sound Cannon would have a rear pipe that is three quarters as long as that-13.5 ft. Double that length is 27 ft. The frequency with a 27 ft wavelength is 41.6.
An 18 ft long Sound Cannon would therefore require a speaker with an Fs of 41.6 Hz or so, if I read the patent correctly.
Peerless makes four XLS models. Two 12 inchers, two 10 inchers.
The Fs for each is, respectively, 18 Ha, 18 Hz, 28 Hz-and 39.4 Hz.
The XLS speaker with the 39.4 Hz Fs would appear to be a good fit for an 18 ft long Sound Cannon. However, it is not a 12 incher, it is a 10 incher.
If Drew can find that article, I would wonder-was it perhaps the XLS 10 incher that was the basis for the Sound Cannon?
I am just speculating here.
PS: SoundEasy-BoxCad, a pay loudspeaker modeling program, can simulate a Sound Cannon enclosure. Now if anyone has that software, please jump right in this conversation.
If I understand the patent correctly, a twelve foot pipe would require a speaker with an Fs of 63 Hz.
An 18 foot pipe Sound Cannon would have a rear pipe that is three quarters as long as that-13.5 ft. Double that length is 27 ft. The frequency with a 27 ft wavelength is 41.6.
An 18 ft long Sound Cannon would therefore require a speaker with an Fs of 41.6 Hz or so, if I read the patent correctly.
Peerless makes four XLS models. Two 12 inchers, two 10 inchers.
The Fs for each is, respectively, 18 Ha, 18 Hz, 28 Hz-and 39.4 Hz.
The XLS speaker with the 39.4 Hz Fs would appear to be a good fit for an 18 ft long Sound Cannon. However, it is not a 12 incher, it is a 10 incher.
If Drew can find that article, I would wonder-was it perhaps the XLS 10 incher that was the basis for the Sound Cannon?
I am just speculating here.
PS: SoundEasy-BoxCad, a pay loudspeaker modeling program, can simulate a Sound Cannon enclosure. Now if anyone has that software, please jump right in this conversation.
More questions
If I use sewer elbows to smoothly bend the tube around a corner, would that cause any problems?
Also, it looks as though you are only designing a subwoofer with a tube on one side of the woofer. What about the Wave Cannon, which has tubes over both sides? Or do you just compute the total length and put the driver a third of the way up the tube?
Does this increase SPL or diminish it?
If I use sewer elbows to smoothly bend the tube around a corner, would that cause any problems?
Also, it looks as though you are only designing a subwoofer with a tube on one side of the woofer. What about the Wave Cannon, which has tubes over both sides? Or do you just compute the total length and put the driver a third of the way up the tube?
Does this increase SPL or diminish it?
BAM:
No, I am computing a configuration for both sides with a tube. the tube in back is The Long Tube, and is 3 times the length of The Short Tube in front.
The wavelength of the resonant frequency of the driver whould be twice the length of the The Long Tube. Or, if you do the math, it should be 1.5 times the length of both tubes put together.
Both tubes put together should be about a quarter wavelength of the lowest frequency you want reproduced.
Put the driver about one quarter the way up the tube, not a third. At least, that is how Bose designed it-I don't what happens if you put the driver one third the way in.
Incidentally, some transmission line enclosures are designed for the driver to be one third of the way up the length of the tube. What would happen with this configuration-one tube in front, one in back-I don't know.
Even after reading the patent, we have lots of unanswered questions.
No, I am computing a configuration for both sides with a tube. the tube in back is The Long Tube, and is 3 times the length of The Short Tube in front.
The wavelength of the resonant frequency of the driver whould be twice the length of the The Long Tube. Or, if you do the math, it should be 1.5 times the length of both tubes put together.
Both tubes put together should be about a quarter wavelength of the lowest frequency you want reproduced.
Put the driver about one quarter the way up the tube, not a third. At least, that is how Bose designed it-I don't what happens if you put the driver one third the way in.
Incidentally, some transmission line enclosures are designed for the driver to be one third of the way up the length of the tube. What would happen with this configuration-one tube in front, one in back-I don't know.
Even after reading the patent, we have lots of unanswered questions.
I René,
I suppose you are from Montreal or somewhere near. Tu parles francais? I am sure you bought this speaker at Addison or Maddison. I have somewhat a good experience with Max pentivents speakers and the one you bought is meant for a small enlcosure. You should have received a spec sheet with the speaker. There are recommend enlcosure volumes and everything you need to know on the speaker. And for this speaker specificaly I don't think you will get deep and loud bass. Not powerful enough.
I suppose you are from Montreal or somewhere near. Tu parles francais? I am sure you bought this speaker at Addison or Maddison. I have somewhat a good experience with Max pentivents speakers and the one you bought is meant for a small enlcosure. You should have received a spec sheet with the speaker. There are recommend enlcosure volumes and everything you need to know on the speaker. And for this speaker specificaly I don't think you will get deep and loud bass. Not powerful enough.
From memory, originally the magazine article suggested using one of the Response brand drivers from Jaycar in Australia.
I don't have the article, it was one I thumbed through in the newsstand. (guilty as charged!) Because I was interested I kept notes of overall pipe length, distance ratios etc.
General reports on the response units are that although they function ok, they aren't the last word in driver quality.
The 8 ohm Peerless 10 inch xls has a better reputation, higher power handling, lower fs etc, etc,etc and a much better built structure if the 12 inch xls I've seen is anything to go by.
________________________________________
Re putting the driver one third of the way along the tube...
the back wave from the driver is opposite in phase to the front wave.
draw a sine wave with a negative peak starting at one side of the driver and have it do 1/2 a wavelength so it produces a positive peak level with the end of the short tube
Now start off a positive peak sine wave of the same frequency in the long tube but here it has a full wavelength's distance to propagate. It'll end up at the positive peak at the end of the tube.
Now sum positive peak from the rear of the short tube with the positive peak from the rear of the long tube...
BOOM!!!
Of course, using a 6m pipe then if you wanted to take someone's teeth out at 85hz it could be fun. And if you had the space for a 24m pipe....
In a nutshell, placing the driver a third of the way along causes mighty big peaks and troughs in the response.
________________________________________
As far as using smooth curves to bend the pipe I see no reason why not. Dr Amar and friends absolutely punish the smoothness of the path in things like the wave radio. (likely to the detriment of the sound due to backwaves IMHO) A straight pipe will be better.
Drew
I don't have the article, it was one I thumbed through in the newsstand. (guilty as charged!) Because I was interested I kept notes of overall pipe length, distance ratios etc.
General reports on the response units are that although they function ok, they aren't the last word in driver quality.
The 8 ohm Peerless 10 inch xls has a better reputation, higher power handling, lower fs etc, etc,etc and a much better built structure if the 12 inch xls I've seen is anything to go by.
________________________________________
Re putting the driver one third of the way along the tube...
the back wave from the driver is opposite in phase to the front wave.
draw a sine wave with a negative peak starting at one side of the driver and have it do 1/2 a wavelength so it produces a positive peak level with the end of the short tube
Now start off a positive peak sine wave of the same frequency in the long tube but here it has a full wavelength's distance to propagate. It'll end up at the positive peak at the end of the tube.
Now sum positive peak from the rear of the short tube with the positive peak from the rear of the long tube...
BOOM!!!
Of course, using a 6m pipe then if you wanted to take someone's teeth out at 85hz it could be fun. And if you had the space for a 24m pipe....
In a nutshell, placing the driver a third of the way along causes mighty big peaks and troughs in the response.
________________________________________
As far as using smooth curves to bend the pipe I see no reason why not. Dr Amar and friends absolutely punish the smoothness of the path in things like the wave radio. (likely to the detriment of the sound due to backwaves IMHO) A straight pipe will be better.
Drew
My idea for a Wave Cannon Project
Say I wanted to build a Wave Cannon using the MCM 55-1854 4" aluminum woofer. (this woofer has a nice low frequency range - all the way down to 50 Hz.)
For an F3 of 56 Hz (above the Fs of 54.1 Hz), how long should I make the 2.5" pipe?
(What I'm asking is, could someone calculate a 1/4-wave for me, or tell me how to calculate it for myself? We haven't covered sound in my physics class yet.)
I will build this during the summer I think, or next Christmas, powered by a 15W/channel (@ 4ohms) amplifier kit from Parts Express. I could make the wave cannons to hang on the underside of my loft in my dorm room and then make little satellites to be where they can point right at me for music in bed.
Say I wanted to build a Wave Cannon using the MCM 55-1854 4" aluminum woofer. (this woofer has a nice low frequency range - all the way down to 50 Hz.)
For an F3 of 56 Hz (above the Fs of 54.1 Hz), how long should I make the 2.5" pipe?
(What I'm asking is, could someone calculate a 1/4-wave for me, or tell me how to calculate it for myself? We haven't covered sound in my physics class yet.)
I will build this during the summer I think, or next Christmas, powered by a 15W/channel (@ 4ohms) amplifier kit from Parts Express. I could make the wave cannons to hang on the underside of my loft in my dorm room and then make little satellites to be where they can point right at me for music in bed.
BAM:
Considering the various things that are unknown here, I would suggest getting an inexpensive 4" and testing. I will do the math for the speaker you specified tomorrow-getting a little late for involved calculations tonight.
I would think the best bet is to find someone who has bought the SoundEasy program, which calculates these things. They even mention the Sound Cannon in the promotional literature.
Considering the various things that are unknown here, I would suggest getting an inexpensive 4" and testing. I will do the math for the speaker you specified tomorrow-getting a little late for involved calculations tonight.
I would think the best bet is to find someone who has bought the SoundEasy program, which calculates these things. They even mention the Sound Cannon in the promotional literature.
The SoundEasy/BoxCAD suite costs $250, so it would be advisable to find someone with the program to help you out on any project that runs into money.
If there were any equations, somebody with more math ability than myself could use Excel or some other spreadsheet to graph things for free. But the patent does not appear to contain equations. I'll re-check, though.
Incidentally, from the promotional literature that Bose itself supplies, I see no evidence that the Sound Cannon, despite it's provacative name, provides any more bass output than a bass reflex enclosure one half it's volume.
If there were any equations, somebody with more math ability than myself could use Excel or some other spreadsheet to graph things for free. But the patent does not appear to contain equations. I'll re-check, though.
Incidentally, from the promotional literature that Bose itself supplies, I see no evidence that the Sound Cannon, despite it's provacative name, provides any more bass output than a bass reflex enclosure one half it's volume.
Re: My idea for a Wave Cannon Project
Sound travels at the rate of 770 miles per hour or so. Slightly slower above sea level. For planes, Mach 1 is the speed of sound, Mach 2 is twice the speed of sound, etc. I believe Mach was the fellow who figured out the speed of sound.
Anyhow, 770 miles per hour figures into 13,500 inches per second. So the wavelength of 1 Hertz is 13,500 inches.
To find the wavelength of any frequency, simply divide 13,500 by that frequency. So the wavelength of 54 Hz is (13,500/54), which is 250 inches.
That is how we find the wavelength of any frequency. However, here we have a speaker with an Fs of 54 and want to find what size tube we need for it. I shall go by the patent-I never built one of these things.
However, The Long Tube is only 75% of the total length of the enclosure. And the total length of the enclosure is 1/4 wavelength of the lowest frequency.
So, we divide 125" by .75, and we find the total length of the tube is 166.66 inches. That is the length of a quarter wavelength of the lowest frequency we are trying to reproduce. So, we multiply the tube length by 4 to find the wavelength of F3. 166.66 inches X 4 = 666.6 inches-the wavelength of F3.
To find F3, we simply divide 13,500 inches by 666.6 inches, and we get 20.25 Hz. That should be the F3 of the speaker in the Cannon enclosure.
Don't forget, the length of the total enclosure is 166.6 inches, or 13.9 feet long. Are you sure you will be able to fit this into your dorm room?
Again, I am just going by what the patent says, or what my interpretation of the patent is.
BAM said:
Sound travels at the rate of 770 miles per hour or so. Slightly slower above sea level. For planes, Mach 1 is the speed of sound, Mach 2 is twice the speed of sound, etc. I believe Mach was the fellow who figured out the speed of sound.
Anyhow, 770 miles per hour figures into 13,500 inches per second. So the wavelength of 1 Hertz is 13,500 inches.
To find the wavelength of any frequency, simply divide 13,500 by that frequency. So the wavelength of 54 Hz is (13,500/54), which is 250 inches.
That is how we find the wavelength of any frequency. However, here we have a speaker with an Fs of 54 and want to find what size tube we need for it. I shall go by the patent-I never built one of these things.
250 inches is the wavelength of of 54 Hz, the resonant frequency of our speaker. That is supposed to be twice the wavelength of The Long Tube. So The Long Tube is supposed to be 125 inches.
However, The Long Tube is only 75% of the total length of the enclosure. And the total length of the enclosure is 1/4 wavelength of the lowest frequency.
So, we divide 125" by .75, and we find the total length of the tube is 166.66 inches. That is the length of a quarter wavelength of the lowest frequency we are trying to reproduce. So, we multiply the tube length by 4 to find the wavelength of F3. 166.66 inches X 4 = 666.6 inches-the wavelength of F3.
To find F3, we simply divide 13,500 inches by 666.6 inches, and we get 20.25 Hz. That should be the F3 of the speaker in the Cannon enclosure.
Don't forget, the length of the total enclosure is 166.6 inches, or 13.9 feet long. Are you sure you will be able to fit this into your dorm room?
Again, I am just going by what the patent says, or what my interpretation of the patent is.
If you are making the tubes a diameter of 2.5", then the circular area of the tubes is 4.9 sq in, and the volume is 816 cubic in, or 47% of a cubic foot. Not bad.
That is if it works. The patent seems to give us guidelines, but not formulas like the ported box uses.
There is the further issue of the ability of a 4" speaker to procduce hearable bass at 20 Hz. I doubt it-the speaker simply cannot move sufficient amount of air, even enhanced by the tube. A ported box enhance the air moving capability of a speaker by four. Even is the Sound Cannon is twice as great as the ported box, you will still fall woefully short.
In it's Sound Cannon going down to 25 Hz, Bose seems to think a 12" woofer with a half inch excursion is necessary. That speaker moves 43 cubic inches of air. Even if your 4" has an excursion of .25"-which it probably does not-you are only moving 1.75 cubic inches of air. And you are trying to go lower than the Bose Cannon!
Why not aim for a Sound Cannon going down to 50 Hz? The tubes will only be 40% as long, and you have a much better chance of getting hearable bass out of it.
That is if it works. The patent seems to give us guidelines, but not formulas like the ported box uses.
There is the further issue of the ability of a 4" speaker to procduce hearable bass at 20 Hz. I doubt it-the speaker simply cannot move sufficient amount of air, even enhanced by the tube. A ported box enhance the air moving capability of a speaker by four. Even is the Sound Cannon is twice as great as the ported box, you will still fall woefully short.
In it's Sound Cannon going down to 25 Hz, Bose seems to think a 12" woofer with a half inch excursion is necessary. That speaker moves 43 cubic inches of air. Even if your 4" has an excursion of .25"-which it probably does not-you are only moving 1.75 cubic inches of air. And you are trying to go lower than the Bose Cannon!
Why not aim for a Sound Cannon going down to 50 Hz? The tubes will only be 40% as long, and you have a much better chance of getting hearable bass out of it.
I finally found the SB articles dealing with this device.
It was back in 1995 (thats why it took me so long to find it: I had to fight my way up to the attic).
It was in issues 6 (page 8) and 7 (page 18), was written by G.R. Koonce and titeled "The waveguide path to deep bass". Unfortunately there is a third part as well, which might be the most interesting of them all, and which I don't own (it was very hard to find "Speaker Builder" in central Europe, the only European place I've seen it so far was in the newspaper department of Tower Records in London).
Regards
Charles
It was back in 1995 (thats why it took me so long to find it: I had to fight my way up to the attic).
It was in issues 6 (page 8) and 7 (page 18), was written by G.R. Koonce and titeled "The waveguide path to deep bass". Unfortunately there is a third part as well, which might be the most interesting of them all, and which I don't own (it was very hard to find "Speaker Builder" in central Europe, the only European place I've seen it so far was in the newspaper department of Tower Records in London).
Regards
Charles
BAM:
The point of my previous post was that your MCM speaker with the 54 Hz Fs wouldn't be able to be used in a Cannon going down to only 50 Hz.
I am just going by my interpretation of what the patent says. I could well be mistaken, but here goes.
We want to know what the Fs of the speaker would be if it was to be used in a Sound Cannon that has an F3 of 50 Hz.
The tubes, both front and back added together, should be a quarter wavelength of 50 Hz. The wavelength of 50 Hz is (13,500/50) = 270 inches. So a quarter of that equals 67.5 inches. The two tubes together should be 67.5 inches long.
The Long Tube should be 3/4 of that length. So The Long Tube should be 50.6 inches long-let us round off to 50 inches.
The wavelength of the resonant frequency of the speaker should be twice the length of The Long Tube. That would make it 100 inches.
13, 500 inches divided by 100 inches yields a frequency of 135 Hz. So to build the enclosure you are speaking of, find a speaker with an Fs of 135 Hz, and have the tube behind it be 50 inches long, and the tube in front of it be 17.5 inches long.
Again, this is just going by the patent, as best as I can understand it.
The point of my previous post was that your MCM speaker with the 54 Hz Fs wouldn't be able to be used in a Cannon going down to only 50 Hz.
I am just going by my interpretation of what the patent says. I could well be mistaken, but here goes.
We want to know what the Fs of the speaker would be if it was to be used in a Sound Cannon that has an F3 of 50 Hz.
The tubes, both front and back added together, should be a quarter wavelength of 50 Hz. The wavelength of 50 Hz is (13,500/50) = 270 inches. So a quarter of that equals 67.5 inches. The two tubes together should be 67.5 inches long.
The Long Tube should be 3/4 of that length. So The Long Tube should be 50.6 inches long-let us round off to 50 inches.
The wavelength of the resonant frequency of the speaker should be twice the length of The Long Tube. That would make it 100 inches.
13, 500 inches divided by 100 inches yields a frequency of 135 Hz. So to build the enclosure you are speaking of, find a speaker with an Fs of 135 Hz, and have the tube behind it be 50 inches long, and the tube in front of it be 17.5 inches long.
Again, this is just going by the patent, as best as I can understand it.
So I could build the 13-foot line but not expect the greatest results? What would become of that little driver if I put it in and asked it to go down to as far as it would go? Would it tear itself apart trying to do 20Hz or would it just be a long line that is still only any good down to 50 Hz?
BAM said:
Don't know. My guess is that things would be no worse than if you put it in a sealed box or ported enclosure that would allow it to go down to 20 Hz. You would be building a long line that would not get used to it's full potential, but if that is what you want to do, go ahead. It's only going to be 2.5" diameter PVC pipe anyway, so I guess it would be relatively easy to snake around the room.
For what it is worth, I believe a major Japanese audio maker once made a five inch speaker in a ported container about a third of a cubic foot, and it was flat down to 30 Hz. Nobody ever reported anything about the speaker tearing itself apart.
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