A pipe expanding in a linear fashion toward the terminus is a conical horn; assuming St = 0, then it has a resonant frequency of 1/2 lambda and both odd and even harmonics. An uptapered pipe has a resonant frequency of 1/4 lambda and produces only odd harmonics. There is no such thing as a 1 1/4 wavelength pipe. There are only 1/2 wave or 1/4 wave pipes.
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I am rapidly getting the feeling that you know exactly what I am talking about.
There is no such thing as a 1 1/4 wavelength pipe. There are 1/4 wave pipes, or 1/2 wave pipes. That's it. You could create a pipe 1.25x whatever the wavelength of a given frequency is, but that is not a 1 1/4 wave pipe. That is either a 1/4 or 1/2 wave pipe tuned to a much lower frequency.
There is no such thing as a 1 1/4 wavelength pipe. There are 1/4 wave pipes, or 1/2 wave pipes. That's it. You could create a pipe 1.25x whatever the wavelength of a given frequency is, but that is not a 1 1/4 wave pipe. That is either a 1/4 or 1/2 wave pipe tuned to a much lower frequency.
I don't get the same feeling.
When I refer to "Wavelength", it is a measure of length, and given a speed of sound and rate of Hz, can be converted to and from meters, inches, feet, etc.
When I refer to a pipe being a certain wavelength (1/2, 1/4, 1 1 1/4, etc), I mean it's length is that multiple of whatever wavelength it is understood we are talking about. This might be the Fs of the driver, a slightly lower sound than the driver's Fs as some suggest, or a completely arbitrary wavelength. A 80Hz quarter wavelength tube is also a 160Hz half wavelength tube. In terms of hypotheticals, we can say we are talking about one and not the other, but if we were to physically build both, they'd physically be the same.
Since a wavelength, or any multiple there of, can be converted to inches, and a tube of that number of inches can be constructed, at least in theory. For a reasonable number of inches (less than 100) it is trivial to build such a tube. Hypothetical discussion of how such a tube behaves with sounds of that wavelength can be valid, interesting and important, even if building such a tube for the purposes of amplifying that wavelength is not a viable design.
My main confusion is how a quarter wavelength tube is a viable design - that is based on my knowledge of physics, a closed tube will have a significant void for sound waves with a wavelength 4 times the length of the tube. If that is the case, it is a poor choice for amplifying those soundwaves.
I realize that a TQWT is not the same as a closed tube, but any different way I've tried to think about it leads me to believe it has a void at for sound waves 4 times its length.
I believe driver placement in a BIB or TQWT design is meant to minimize certain harmonics. I have no idea how .217 was chosen as the ideal driver placement, or why this placement performs better than most randomly chosen locations.
I suggest you read the pages I linked to, particularly the many detailed papers on Martin King's site (Quarter Wavelength Loudspeaker Design).
I have. Anything in specific? There is a lot of material here.
Take a look at the graphic on the first page that shows the standing waves. In your head, draw the wave reflections for the red line assuming the "open end" reflects without phase shift. The closed end might phase shift 180 degrees or it might not phase shift at all. Either way, the reflected waves create a void.
Paul Voigt wrote in his patent:
Is it possible he wasn't trying to use the reflected waves from the open end to build resonance at all? Other parts of the patent (mention of corner placement being radiation into 1/8th of a sphere) hint that he is maybe using the room itself. If he is trying to build resonance similar to room modes and believes 1/4 wavelength will be constructive, stopping just short of that length would be one of the worst things he could do. Perhaps he knew 1/4 length would have a void, and deliberately stopped short of this length to avoid that it? He is definitely writing about mass-loading his driver with the column of air. I also get the impression he is building a tube around a wave several octaves lower than the Fs of the driver he is using.
Is it possible what actually did, what people building TQWT today believe he did, and what people building TQWT are building today rely on completely different physics, even if these designs are all implemented as a tube about 1/4 the length of Fs? Of course any of these designs have properties of a transmission line, a horn and a base reflex and any number of properties (useful or detrimental) that their designer didn't intend. Martin King seems to hint at this last point.
Is it possible he wasn't trying to use the reflected waves from the open end to build resonance at all? Other parts of the patent (mention of corner placement being radiation into 1/8th of a sphere) hint that he is maybe using the room itself. If he is trying to build resonance similar to room modes and believes 1/4 wavelength will be constructive, stopping just short of that length would be one of the worst things he could do. Perhaps he knew 1/4 length would have a void, and deliberately stopped short of this length to avoid that it? He is definitely writing about mass-loading his driver with the column of air. I also get the impression he is building a tube around a wave several octaves lower than the Fs of the driver he is using.
Is it possible what actually did, what people building TQWT today believe he did, and what people building TQWT are building today rely on completely different physics, even if these designs are all implemented as a tube about 1/4 the length of Fs? Of course any of these designs have properties of a transmission line, a horn and a base reflex and any number of properties (useful or detrimental) that their designer didn't intend. Martin King seems to hint at this last point.
Rooms are 1/2 WL resonators, so to damp a driver's Fs with a 1/2 WL resonator requires it to be 4x longer than a 1/4 WL resonator.
The 1/4 WL resonator has historically been used to damp the driver's Fs impedance. Paul stopped it physically 'short' no doubt because its acoustical path-length is longer, i.e. there is an end correction that must be factored in and if heavy damping is used, then the pipe's physical length must be further shortened to match up to its acoustic path-length.
Nowadays, most folks don't need to tune to Fs to maximize bass efficiency, so one can use the pipe's harmonics combined with driver offset to shape the driver's response. Ditto for 1/2 WL resonators.
No, the physics hasn't changed nor our basic understanding of them.
GM
I played with some real tubes last night, and was sadly disappointed. I am able to get resonance at both 1/2 and 1/4 wavelength, but 1/2 is stronger and I only measured +3db. I am sure I can do better with a real enclosure, but I just don't think the design tradeoffs are worth it. Without damping, I get a hall-of-echos effect that I am certain can be minimized but I am not sure can be eliminated, the response graphs I've seen of transmission lines all look a little ragged. Also a thin 7 foot tube that minimizes floor space looks a lot better on paper than in my living room, and a folded tube takes up too much floor space and puts the tweeter at the wrong level. What do I gain for all this? I think I can more/better bass just using a bigger woofer and a sealed box. The cost of the woofer and crossover isn't much when you consider the time and cost to build the box. I am sure transmission lines have a place in the audio world, but probably not for me.
I did read the Anatomy of a TL paper in more detail. There is no explanation of physics, the author even suggests "an undergraduate level vibration textbook" for those like me who don't understand everything before reading the paper.
The wikipedia article is a better introduction, and clearly states the resonance of various cylinders and cones, but does not explain why they resonate.
I guess if I really want to understand this, I need to pick up an acoustics textbook. One idea I had is sound waves are not really sine waves, but more a sine and inverted sine wave together - so the anti-nodes are all the same regardless of phase. This makes a 180 degree phase-shift constructive instead of destructive, and fits everything I've read so far.
I did read the Anatomy of a TL paper in more detail. There is no explanation of physics, the author even suggests "an undergraduate level vibration textbook" for those like me who don't understand everything before reading the paper.
The wikipedia article is a better introduction, and clearly states the resonance of various cylinders and cones, but does not explain why they resonate.
I guess if I really want to understand this, I need to pick up an acoustics textbook. One idea I had is sound waves are not really sine waves, but more a sine and inverted sine wave together - so the anti-nodes are all the same regardless of phase. This makes a 180 degree phase-shift constructive instead of destructive, and fits everything I've read so far.
I suggest trying this simulator:
Ripple Tank Simulation
It's a Java based simulator of the old school physics "ripple tank". It has a number of built-in examples to try.
Read all the notes before trying. Check out the "3D mode" which clearly illustrates the positive and negative pressures and how cancellation works.
Note: Due to the current Java based Internet exploits, you probably have (and should have) Java disabled in your browser. If so, you won't see the simulation when you go to the page. In that case, either enable Java for that page or download and run the app locally.
- Download the ZIP file.
- Create a folder and unZIP the files into it.
- You will have a local copy of the Web pages plus the Ripple.jar file. If you have Java installed, double-clicking on the .jar file will run the application.
Ripple Tank Simulation
It's a Java based simulator of the old school physics "ripple tank". It has a number of built-in examples to try.
Read all the notes before trying. Check out the "3D mode" which clearly illustrates the positive and negative pressures and how cancellation works.
Note: Due to the current Java based Internet exploits, you probably have (and should have) Java disabled in your browser. If so, you won't see the simulation when you go to the page. In that case, either enable Java for that page or download and run the app locally.
- Download the ZIP file.
- Create a folder and unZIP the files into it.
- You will have a local copy of the Web pages plus the Ripple.jar file. If you have Java installed, double-clicking on the .jar file will run the application.
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Bvbellomo,
If you don't see how a quarter wave or half-wave resonator does anything, look at any woodwind/brass instrument and you will see how sound wave amplification works by taking the tiny vibrations caused by air flowing across an edge to oscillate and drive the air column inside the instrument to make a big sound. How loud is the sound of pursed lips blowing in plain air versus blowing in a tuba, trombone, french horn? If you play with the simulation tools, there are 10 to +15 dB gains to be had in the bass region with a back loaded horn or transmission line. Sure, a plain straight pipe TL will have terrible peaks and dips, but the point of good design is to mitigate all those things. Look at the predicted response curves of the many excellent designs that folks on this forum have produced and you will see that the peaks and valleys are for the most part, minimal. Look at the response curve for the TABAQ MLTL - it is flat as a board. I wouldn't dismiss the TL's or BLH's based on your experiments with simple straight tubes. And they are not bulky or large either so I am not sure why you say they take too much floor space. The Cornu BLH is a wall mount flat speaker and takes zero floor space.
If you don't see how a quarter wave or half-wave resonator does anything, look at any woodwind/brass instrument and you will see how sound wave amplification works by taking the tiny vibrations caused by air flowing across an edge to oscillate and drive the air column inside the instrument to make a big sound. How loud is the sound of pursed lips blowing in plain air versus blowing in a tuba, trombone, french horn? If you play with the simulation tools, there are 10 to +15 dB gains to be had in the bass region with a back loaded horn or transmission line. Sure, a plain straight pipe TL will have terrible peaks and dips, but the point of good design is to mitigate all those things. Look at the predicted response curves of the many excellent designs that folks on this forum have produced and you will see that the peaks and valleys are for the most part, minimal. Look at the response curve for the TABAQ MLTL - it is flat as a board. I wouldn't dismiss the TL's or BLH's based on your experiments with simple straight tubes. And they are not bulky or large either so I am not sure why you say they take too much floor space. The Cornu BLH is a wall mount flat speaker and takes zero floor space.
I am not saying it doesn't work, just that I don't understand how. Some of the best physicists today say they don't understand gravity, yet none are in fear of floating away into the sky.
I played around with the app, and will some more, but don't see how to edit the model numerically. Just drawing walls with my mouse and adjusting a slider for frequencies is of very limited use.
Wall-mounted anything may be out do to WAF.
Google some tutorials on how to use HornResp - very helpful in getting started. You should not be using mouse with slider to start. The design should be manually entered as a series of areas, lengths, type of expansion based on an initial design that you come up with in sketch using rules of thumb or a starting known design from someone else.
How it works is the based on acoustic wave propagation theory, which is based on fluid mechanics, which is based on the Navier-Stokes equations, which is nothing more than an implementation of Newton's second law: F=ma, plus the conservation of mass equation. So we do indeed understand it all the way down to the governing equations. You may say we do not understand why F=ma works (like F_gravity=c x m1 x m2 / r^2. Those are phenomenological relations and cannot yet be proven, hence they are called "Laws". But that is irrelevant and should not stop one from using the relationship which for the most part works very well at describing the universe and has been used for successfully designing and making things like airplanes, rockets, cars, bridges, satellites, speakers, etc. Get to quantum levels and we use different equations...
How it works is the based on acoustic wave propagation theory, which is based on fluid mechanics, which is based on the Navier-Stokes equations, which is nothing more than an implementation of Newton's second law: F=ma, plus the conservation of mass equation. So we do indeed understand it all the way down to the governing equations. You may say we do not understand why F=ma works (like F_gravity=c x m1 x m2 / r^2. Those are phenomenological relations and cannot yet be proven, hence they are called "Laws". But that is irrelevant and should not stop one from using the relationship which for the most part works very well at describing the universe and has been used for successfully designing and making things like airplanes, rockets, cars, bridges, satellites, speakers, etc. Get to quantum levels and we use different equations...
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