What is the math(s) used to design the waveguides behind the Nautilus loudspeaker. Is it a 1/4 wave design that tapers to a point? Does volume not matter? Is it a sealed or t-line enclosure? “Experiments showed that tapering the horn shape and then curling it up would perform just as well but would occupy a much smaller volume than a straightforward, constant cross-section pipe. ”
This got truncated. :/
@Bmsluite
I’m looking at those curves on my phone so excuse me if I not seeing things properly.
If β denotes the measurements with the shaped baffle. of the improvement seems to be in the region above ~1KHz.
@fluid
The designs of B&W, as a company, may seen a little, err, inconsistent. But when viewed through the lens of the people working the company, it makes a little more sense.
After releasing the 801 in 1979, 3 way box with minimal baffles and 45 degree facets.
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I’m looking at those curves on my phone so excuse me if I not seeing things properly.
If β denotes the measurements with the shaped baffle. of the improvement seems to be in the region above ~1KHz.
@fluid
The designs of B&W, as a company, may seen a little, err, inconsistent. But when viewed through the lens of the people working the company, it makes a little more sense.
After releasing the 801 in 1979, 3 way box with minimal baffles and 45 degree facets.
This got truncated. :/
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A TL is a resonator. The Nautilus is the exact opposite, it is designed to absorb the back emitted sound.
I think it’s a highly damped sealed enclosure of odd dimensions. Especially when you consider the Nautilus uses lots of eq in the bass. But, I could be wrong.
To be fair B&W call it a transmission line. The tubes for the high frequency units are reverse horns. Maybe it’s all marketing like @Arez says.
To be fair B&W call it a transmission line. The tubes for the high frequency units are reverse horns. Maybe it’s all marketing like @Arez says.
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Some TLs are, some aren’t. If it is damped aperiodic, which the Nautilus is, the are (close to) not resonance.
Theback wave passes thru a half-wavelength of damping as it goes down the line, then another half wavelength on the way back — by the time it gets back to the driver it has been (larely) damped out/killed.
dave
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Only if it's designed to be. Many are used for that purpose -nobody ever said that is some form of obligation. You might recall the title of Arthur Bailey's Wireless World article (the one many tout as the first and annouce as the only arbiter of what a TL is): 'A Non-Resonant Loudspeaker Enclosure Design'. 😉
Aperiodic TLs are designed with the sole object of providing a response similar to a sealed box, potentially with a little more extension (e.g. Augspurger's alignments) and / or simply the flattest possible impedance curve; sealed TLs typically follow that or (related) a heavily / progressively damped line to kill the back-wave. This is neither news or unusual: 1/2 wave pipes go back to the 1930s.
1/2 wave line; per the above it's not designed for output, just as an alternative to a [in this case] critically damped sealed box with a more effective, if rather bulky way of damping out the back-wave & potentially providing a flat[ter] impedance.
Also TLs of a different kind, in their case 1/4 wave as IIRC they're open tapered pipes, but of highly restricted dimensions, again because the object is damping rather than output. The implementation has a heavy dose of marketing (they're a commercial company, not a charity) but the actual operating physics are perfectly functional. Whether it's necessary is another matter. But you can say that in some way about about many commercial products or DIY productions.
So the progressively stuffed reverse closed horn is a 1/2 wavelength aperiodic transmission line. I’m guessing the drawback is less lower bass.
Edit, and I can figure out that math. That is, If I want to try it.
Edit, and I can figure out that math. That is, If I want to try it.
The maths for an optimised version is going to be pretty tricky. The task being how to change the impedance via area change and density of damping material (and type) to minimise reflection while maximising absorption. The tubes are of course primarily a marketing feature but that doesn't mean working out to make them work well won't be fun.
Martin King, Hyperphysics (& another bod who's name has shamefully escaped me as I've yet to have some caffine this morning, but wrote a paper on the subject decades ago) etc. have already done most of that; you can model them in Hornresp, Akabak etc. easily enough. Re 'less lower bass' -depends to a point on less that what in particular; the limit of reinforcement is roughly that of other forms of sealed enclosures so if that's the requirement a different type of load will be needed.
How to maximise absorption while minimising reflection is a fairly common problem in acoustics (e.g. anechoic walls, non-reflecting boundary conditions, perfectly matched layers, etc...) so the maths can be looked up to a fair extent but it will depend on the model for dissipation adopted. My experience with absorbing layers and boundary conditions for numerical solvers has been that maximising performance is not straightforward. The more general models for acoustic absorption are likely to be relevant if one is chasing maximising high performance.
I would agree that hornresp (if you have access to a Windows computer) is likely to be a good way to get a handle on what is going on but it is sidestepping the maths which Arthur was considering figuring out and I was suggesting was tricky if he wanted to optimise performance.
I would agree that hornresp (if you have access to a Windows computer) is likely to be a good way to get a handle on what is going on but it is sidestepping the maths which Arthur was considering figuring out and I was suggesting was tricky if he wanted to optimise performance.
Well, as I mentioned, Martin King, George Augspurger, Terman, Olney & to a point Leach (along with resources like Hyperphysics) have done most of the the spade-work on that front with their various papers / articles / patents as-relevant, so are good initial ports of call. A progressive damping ratio is usually preferable in untapered types; a contracting type tends to provide that automatically for a given quantity & spacing of volume fill so trying to increase the damping quantity close to the narrowest part of the pipe tends to be both difficult in practice & result in over damping -until you reach the point where it starts acting like a solid & you end up going the other way again. 😉
The people you cite (OK the couple I have looked at in the past!) make significant assumptions about the form of damping in porous media. A perfectly reasonable thing to do if one wants to get on with things and doesn't want the maths to get tricky but I would suggest it is not a good place to start if you wish to model damping well. When you examine many, perhap most, detailed models involving acoustics it is the damping that tends to limit the accuracy achievable. Years ago I was briefly in touch with someone involved in a project Scan-Speak put out to various groups to simulate in detail a 2" driver of theirs. The broad conclusion told to me was that the damping wasn't adequately modelled. Not sure it was ever published externally but would be good to see. Anyone? The conventional linear TS model for a driver uses viscous damping to model the suspension which leaps out as poor. Structural damping and fluid damping tend to be very different. I guess it "works" because the value is determined from the peak of the driver resonance where it is correct and although it's variation with frequency is going to be poor it tends not to be a significant term except at low frequency impedance peak/s.
Probably depends what you call 'significant assumptions'. George Augspurger took detailed empirical measurements of various damping materials at various densities & derived coefficients from that; Martin did the same for Dacron up to 1lb/ft^3. They've proved extremely accurate for the last 25 years, so I'd say their measured data & derivations aren't a bad place to start.
There's potentially a danger in over-thinking this, so I suppose it depends where your priorities lie. Yes, Martin, George & others derived (very accurate, within the boundaries they used) coefficients based on their empirical testing and did not necessarily grind back to the very basic physical principles & then work up from there. But there's a reason for that: what they did was / is fit for purpose, & going further wasn't really necessary. We could say the same for T/S parameters, which I'd actually be inclined to call more, not less, problematic given that some units can show signficant variations with drive level -but then, Thiele (& later Small) always stressed they were created under small-signal assumptions; the later arguments of Scan, Seas etc. that they should be measured at higher voltage drives have merit as it's arguably more representative of real world conditions, but opens things up to greater variation across the board. By and large though, the simplifying T/S equations may not necessarily be as refined as progressively breaking every possible area down to fundamental values -but in the vast majority of situations they're good enough for purpose. I'm a self-confessed brontosaurus 🦕 so for me, good enough is good enough: perfect is usually a pain in the backside & since most of the time the massive extra effort doesn't bring any significant [or any, period] useful gains for a real-world application, when it gets to that stage, I call it a day as that's what I tend to value.
There's potentially a danger in over-thinking this, so I suppose it depends where your priorities lie. Yes, Martin, George & others derived (very accurate, within the boundaries they used) coefficients based on their empirical testing and did not necessarily grind back to the very basic physical principles & then work up from there. But there's a reason for that: what they did was / is fit for purpose, & going further wasn't really necessary. We could say the same for T/S parameters, which I'd actually be inclined to call more, not less, problematic given that some units can show signficant variations with drive level -but then, Thiele (& later Small) always stressed they were created under small-signal assumptions; the later arguments of Scan, Seas etc. that they should be measured at higher voltage drives have merit as it's arguably more representative of real world conditions, but opens things up to greater variation across the board. By and large though, the simplifying T/S equations may not necessarily be as refined as progressively breaking every possible area down to fundamental values -but in the vast majority of situations they're good enough for purpose. I'm a self-confessed brontosaurus 🦕 so for me, good enough is good enough: perfect is usually a pain in the backside & since most of the time the massive extra effort doesn't bring any significant [or any, period] useful gains for a real-world application, when it gets to that stage, I call it a day as that's what I tend to value.
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What's the point of ½ or 1/4 wave here? Each driver has quite wide passband...
Open back of TL are designed to work as bass reflex at certain tuning F, but closed... I think aperiodic is better description here. I amnot sur about mid's tubes, do they havea small hole at the end of the horn?
Open back of TL are designed to work as bass reflex at certain tuning F, but closed... I think aperiodic is better description here. I amnot sur about mid's tubes, do they havea small hole at the end of the horn?
Its 1/2 wavelenght resonator. At resonant frequency air inside behaves both as mass and as spring.
Assuming its resonant frequency is equal to Fs, in effect you have additional mass and stifness added to the cone assembly.
Compared to the closed box, only Q of the system will go up, but not the system resonant frequency. Also, beacuse of dual behaviour of air at resonance, stuffing the line gives more efective acoustical damping of the whole system.
So, with proper design, you can get lower Fs and better damping compared to closed box, and with smaller volume.
Just my few thoughts.
Assuming its resonant frequency is equal to Fs, in effect you have additional mass and stifness added to the cone assembly.
Compared to the closed box, only Q of the system will go up, but not the system resonant frequency. Also, beacuse of dual behaviour of air at resonance, stuffing the line gives more efective acoustical damping of the whole system.
So, with proper design, you can get lower Fs and better damping compared to closed box, and with smaller volume.
Just my few thoughts.