Agreed.
But if it makes you feel better, you can always staple some cardboard egg-carton halves inside your DIY loudspeaker. They will probably be as (in)effective as the expensive one-inch waves in terms of absorbing internal sound.
That old 1972 Bailey transmission-line design uses a clever trick borrowed from geometrical optics (ray optics), namely, directing a wave into an ever-narrowing wedge-shaped space.
If you trace the path of reflections in such a space (see attached hand-drawn image), the (purple) wave bounces back and forth more and more frequently as the space between the wedge walls (black) tapers towards zero, so that you get, in theory, an infinite number of reflections before the wave reaches the pointed end of the wedge.
(For an analogy, imagine summing the series 1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 +......, which goes on for an infinite number of terms, with every term smaller (half) the previous term. There are an infinite number of terms in the series, but, as some of you might remember from high school math, they all sum up to a finite number. In the same way, an infinite number of bounces between the wedge-shaped walls occurs in a finite length of wedge!
Getting back to the ray bouncing between those walls, if you lose even a little energy to absorption on each bounce (which you always do), then an infinite number of bounces will absorb all the energy, leaving nothing! No energy left to bounce back and interfere with the ray that came in.
In practice, of course, you don't get an infinite number, just a very large number. And you don't get 100% absorption of the wave, but you do get almost 100% absorption.
So this sort of tapered wedge-shape behind the speaker is a pretty clever way of absorbing most of the rear sound radiation from the speaker. (Much more effective than generic wavy walls.)
-Gnobuddy
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This problem with this thinking is that it assumes that sound radiates as a focused beam like a laser pointer. In reality sound radiates with a spherical wave front and the further it travels the larger the diameter of the sphere. At some point, the sphere becomes large enough in diameter that it reaches both sides at virtually the same moment and the 'infinite bouncing' ceases, the contributions from left and right walls become in-phase and you get a reflection back.
edit: this is probably not technically 100% accurate but I think it gets the point across
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Tapered sealed TLs can be effective if implemented well, but they're often over-simplified, and in some cases a simple sealed box will do the same job just as well in practical conditions. If you have the space then a max-flat impedance line by definition works extremely well; usually these do not need to be either tapered or especially long. However, with a similar Vp a relatively long line, tapered or otherwise, can have a similar effect with a reduced stuffing density.
That image makes me think of B&W Nautilus stuff... long tubes with an exponentially decreasing cross sectional area. Under some assumptions (plane waves, near parallel walls, infinite length) that would give a linearly increasing acoustic impedance, gradually matching the acoustic impedance of air to a rigid termination,. So sound reflection is low. It's similar to how horns used to be designed using the Webster equation.
Diffraction is not a problem here, chamfering eliminates cavities and eases air flow near the speaker membrane. More flat mid band, confirmed with measurements.
That's basically what B&W were after. Although technically for the mimimal reflection it needs to be full-sized just as a horn does. So lagging / stuffing still needed, & why TBH you can get more or less equivalent results with a short untapered max-flat impedance pipe with a higher packing density. That doesn't look as impressive though.
It does make a difference, quit esignificant but how effective is relative to the nature of the basket at the rear.
dave
The wave front you drew is perpendicular to the direction of propagation of the wave.
The purple arrow I drew is what is called the propagation vector in contemporary terminology.
When the wavefront is a small diameter sphere, the direction of propagation varies from one location on the sphere to another, i.e., the propagation vector varies from one place to another (in direction).
When the wavefront is a very large diameter sphere, it is nearly a flat plane, and the propagation vector description becomes very good in any one small area.
So in fact, when the wavefront is a very large diameter sphere, the ray description is more accurate, and the idea that the ray bounces infinitely many times is closer (rather than farther) from reality.
Unfortunately, it gets the wrong point across!
I agree, neither the ray nor the wavefront description is 100% accurate. To be 100% accurate, you solve the second order differential equation that describes sound waves, applying the proper boundary conditions (zero air velocity at the surfaces of the walls of the tapered horn.)
Richard Feynman gave one of his famous lectures on the sound wave equation, and derived the one-dimensional version of this wave equation with his usual amazing clarity of thought and description: The Feynman Lectures on Physics Vol. I Ch. 47: Sound. The wave equation
In our case, we would need to use at least the two-dimensional equation (both x and y) since we have to deal with two non-parallel walls. With the right software, this would not be hard today. But while you would get pretty accurate results, the process would be obscure enough to make it relatively hard to understand what was going on.
That's why I used the simple geometric ray-tracing approach. It is not 100% accurate, sure, but is "accurate enough" to give some intuitive understanding of the problem, as long as the wavelength is sufficiently small compared to the horn, and the wavefront radius is large enough to be nearly plane compared to the diameter of the horn.
Ths simple ray picture isn't exact, of course. There won't be an infinite number of bounces in the real world, but this is most likely because the tapered shape eventually narrows down until it is smaller than a wavelength, and ray optics ceases to be applicable.
The main point I wanted to make was that a long wedge-shaped space is much more effective at absorbing unwanted radiation than a smoothly wavy surface of the sort that started this whole thread.
Also, as several people have mentioned, acoustic foam or wool positioned where there is the most air velocity inside the box is much more effective than treating the internal surfaces of the box themselves, where air velocity is very low.
As an aside, when it comes to loudspeakers, I don't think we should take any one idea or methodology too seriously - there doesn't seem to be one single best possible way to make a speaker. Often focusing too hard on perfecting one single technical aspect ends up making everything else worse, and you end up with a bad speaker.
-Gnobuddy
Guys, this is what I'm here for - I love to read your posts on stuff I don't have any grasp on myself.
Please keep the discussion going as I learn from every single post here
But looking at my original question, the thing I take away from your responses is that with a kit like the one I aim to build (Monacor Diva Simone), it wouldn't pay off taking all the effort to make the cabinet like that with irregular shapes... Other improvements would be much more beneficial (like picking a more expensive / high quality kit)... Right?
Please keep the discussion going as I learn from every single post here
But looking at my original question, the thing I take away from your responses is that with a kit like the one I aim to build (Monacor Diva Simone), it wouldn't pay off taking all the effort to make the cabinet like that with irregular shapes... Other improvements would be much more beneficial (like picking a more expensive / high quality kit)... Right?
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