I think you are confusing bending of the wavefront with diffraction due to scattering (i.e., secondary waves) at a sharp transistion, for which the smooth curvature is trying to avoid.
pooge said:
No - "scattering" happens every time bending / diffraction happens – its just a gradual matter for both
Michael
Why do you want to continue to confuse the issue??
While your general view of diffraction *may* be valid, you continue to compare apples with oranges.
The wall curvature is meant to minimize scattering from the walls.
If you want to argue about diffraction from the changing curvature of the wavefront, that is different matter, whether or not the underlying phenomenon is the same.
While your general view of diffraction *may* be valid, you continue to compare apples with oranges.
The wall curvature is meant to minimize scattering from the walls.
If you want to argue about diffraction from the changing curvature of the wavefront, that is different matter, whether or not the underlying phenomenon is the same.
pooge said:
No - I stated that Earl is confuse in this very matter.
Its been me who has emphasised to look at the complex of "diffraction > reflection > delay > interference" IIRC.
This – in the end - is what counts to the listener.
pooge said:
No – this is just Earls assumption about OS - but not mine.
And again – lowest HOM ever – lowest diffraction ever – lowest scattering ever – even if it were true (which isn't IMO) for OS - it would not mean a thing unless you document *where* it happens, *how much* happens, and how all of this translates to Swiss cheese defects in our listening area.
As I said earlier – there is a distinction needed between the term (diffraction) describing a mechanism and the term describing a bunch of effects *due to* that mechanism.
Its not apples and oranges – its a whole fruit-punch we have to look at!
😀
Way the best approach IMO is to analyse sound field over frequency – a statement like "lowest diffraction contour" is way misleading to outright wrong in its simplification IMO - only good for another century of ongoing "superiority" discussion.
I'm not talking down OS – as I respect the positive aspects Earl found out and soongsc implemented in his contour that I really love in the app I have (and I'm working on for further refinement) - I just want to put into perspective some outright misleading claims that usually come along like carved in stone.
Michael
I think you are the one misleading with your convoluted manner of communication and hellbound desire to win an argument.
pooge said:
Here! Here!
Just got back from DC. Nice place, I really love downtown Washington (hate the traffic!!).
As I have already pointed out all wavefronts that are transformed from one curvature to another have undergone the same amount of scattering, but not the same amount of diffraction.
You can of course argue that in the end all curves are the same for infinite length but there is not much point in it because we are talking about a real world device that has to radiate into the outside air.
Thus if it has the required characteristic at infinity it is of not much use to us since we want the smallest practical finite device and the length over which we can obtain our scattering is in practice quite short.
The thought that I had is that the o.s. curve might be the shortest curve to join two points with dissimilar slope, but is it the smoothest one?
Rcw.
You can of course argue that in the end all curves are the same for infinite length but there is not much point in it because we are talking about a real world device that has to radiate into the outside air.
Thus if it has the required characteristic at infinity it is of not much use to us since we want the smallest practical finite device and the length over which we can obtain our scattering is in practice quite short.
The thought that I had is that the o.s. curve might be the shortest curve to join two points with dissimilar slope, but is it the smoothest one?
Rcw.
rcw said:
I'll let Earl answer that definitively, but I think being the smoothest slope is the whole idea. I don't think being the shortest has anything to do with it. The waveguide angle and throat opening may define the length, so the walls do not shadow the throat.
The OS curve is what is called a catenoid for a curve with fixed slopes at the end points.
RCW
I have to ask, maybe again, but how do you define "scattering" as opposed to "diffraction". In physics, scattering usually refers to the sound energy reflected off of an object. Now this could include diffraction if we are talking about the "shadow zone", but I do not see the two things as completely seperate.
When a wave propagates down a waveguide it bends to keep itself in contact with and parallel to the walls - this is the boundary condition. No matter what, at some wavenumber, this cannot be true and a second wave is estabished to enforce the boundary condition. Now this wave can be called "scatering from the walls, or diffraction from the walls, whatever, the the net result is the presence of a second mode of wave propagation, one that reflects from the boundary. I call this wave an HOM, others seem to want to call it something else. OK, but I'll continue to call them HOM because that's what they are. Its not really so complicated.
RCW
I have to ask, maybe again, but how do you define "scattering" as opposed to "diffraction". In physics, scattering usually refers to the sound energy reflected off of an object. Now this could include diffraction if we are talking about the "shadow zone", but I do not see the two things as completely seperate.
When a wave propagates down a waveguide it bends to keep itself in contact with and parallel to the walls - this is the boundary condition. No matter what, at some wavenumber, this cannot be true and a second wave is estabished to enforce the boundary condition. Now this wave can be called "scatering from the walls, or diffraction from the walls, whatever, the the net result is the presence of a second mode of wave propagation, one that reflects from the boundary. I call this wave an HOM, others seem to want to call it something else. OK, but I'll continue to call them HOM because that's what they are. Its not really so complicated.
Looking at the paper by Berners and Smith, (’On the use of the Schroedinger equation in the analytic determination of horn reflectance”), they outline a method of modelling the impedance of horns of arbitrary cross section by cascading conical sections and defining the places where these join as scattering junctions.
This has some useful features such as the “kr” number of the acoustic field at the point where these sections meet is easily defined and also the relationship between wavefront curvature, scattering and diffraction is easily defined and envisaged.
If you consider the case where the wall curve is defined by a continuous function, i.e. the number of conical sections converges on infinity as a limit, then the notion of scattering junctions between these sections also does.
This last feature now has scattering as being defined as occurring along a surface, and since the diffraction is usually defined as the square of the scattering amplitude a fairly simple model allows you to get a good idea of what sort of surface allows you to get the required amount of curvature with the minimum amount of diffraction, and in the case of a near field device get a good approximation to its directivity.
What I also did was consider the field as being defined by complex solutions to the Laplace equation, this is valid since at t=0, the wave equation reduces to this and you can re introduce a time dependant term by stealth with the kr number.
Rcw.
This has some useful features such as the “kr” number of the acoustic field at the point where these sections meet is easily defined and also the relationship between wavefront curvature, scattering and diffraction is easily defined and envisaged.
If you consider the case where the wall curve is defined by a continuous function, i.e. the number of conical sections converges on infinity as a limit, then the notion of scattering junctions between these sections also does.
This last feature now has scattering as being defined as occurring along a surface, and since the diffraction is usually defined as the square of the scattering amplitude a fairly simple model allows you to get a good idea of what sort of surface allows you to get the required amount of curvature with the minimum amount of diffraction, and in the case of a near field device get a good approximation to its directivity.
What I also did was consider the field as being defined by complex solutions to the Laplace equation, this is valid since at t=0, the wave equation reduces to this and you can re introduce a time dependant term by stealth with the kr number.
Rcw.
rcw said:
RCW
I am familiar with this paper. It is good for determining impedance, but NOT for determining directivity or wavefront shape. It really has no relevance to this discussion. The terminology is from "Quantum Mechanics" and is ill applied to the waveguide problem. "Scattering" does have a meaning in terms of the "scattering" matrix as discussed in that paper, but the full 3-D application of the wave equation is far more applicable, and accurate, to the situation under discussion.
The point here is that the waveguide equations for the OS waveguide are exact. Everything else has some approximations somewhere. Hence, the OS solutions as I present in my papers has to be assumed to be the "correct" solution and all else compared to it for accuracy. In all numerical situations the analytically exact solution is taken as the benchmark.
Pooge - "perpendicular" or "parallel" depends on the reference. here I am taking about the waves direction, or the "k" vector. If you are talking about the "wavefront" then, yes, it is perpendicular.
rcw said:
Yes OS seems to be the most efficient contour in transforming plane to spherical at shortest (if we accept the "transition zone" to be considered to do "the most" of the transition wanted) – but not necessarily the "shortest curve to join two points with (!any!) dissimilar slope" IMO
What comes in is the throat dimension for the exit of the plane wave front.
If you make the throat small – I mean veeeery small - you get a OS that diverges to a section of a point source with a veeeeery sharp bending for the "transition part" – meaning the whole OS is kind of diffraction generating (!) device – if you look at it from that point of view.
Not saying that the sound filed created couldn't be what you are after – just to contrast that its not "minimising diffraction or scattering or HOM" that counts alone (we would still have the problem with defining "minimising" with respect to all this terms if we sum up for the whole contour).
This diffraction generating (!) aspect of the OS contour immediately becomes clear if you put a LeCleach of veeeery small throat in comparison.
pooge said:
As for me I wouldn't agree..
gedlee said:
Me too, actually you cant have one without the other – two sides of the same coin...
gedlee said:
Don't think that there is a certain amount of bending / diffraction you can establish as a limit where scattering occurs above – this is a mis-concept of yours IMO as all here is totally gradual - the "second waves" you call HOM (I prefer the concept / picture of "second sources" to look at this) are present *anytime* you bend a wave front - be it OS or any other contour.
Michael
mige0 said:
Once again you ignore everything to make an argument.
You ignored the fact that Earl made a wavenumber qualification.
You ignored the fact that no one has said that a curve will not cause any diffraction.
You ignored the fact that Earl is using foam to clean up what HOMs ARE generated due to the curve, after minimizing these HOMs as much as possible with the smoothest curve.
You are getting SO close to a click of the ignore button.
If you look for instance at the 1.5.kHz. Waveguide I described in my waveguide article.
The wall consists of a single circular arc that starts at 45 degrees and meets the baffle at right angles, using the complex Laplace equation simplification I predicted that this would have constant directivity, and it does.
From the considerations of scattering relations I also predicted that for two dimensions the wall second derivative should be constant for a minimum of diffraction with a given amount of scattering over a finite length, and for a three dimensional axis symmetric device it should be the wall contour squared that is constant, i.e. the o.s. waveguide, not bad for something that is of no use.
What these are is generalisations, a meta calculus if you like, of the wave equation solutions, and I do know the origin of them.
Rcw.
The wall consists of a single circular arc that starts at 45 degrees and meets the baffle at right angles, using the complex Laplace equation simplification I predicted that this would have constant directivity, and it does.
From the considerations of scattering relations I also predicted that for two dimensions the wall second derivative should be constant for a minimum of diffraction with a given amount of scattering over a finite length, and for a three dimensional axis symmetric device it should be the wall contour squared that is constant, i.e. the o.s. waveguide, not bad for something that is of no use.
What these are is generalisations, a meta calculus if you like, of the wave equation solutions, and I do know the origin of them.
Rcw.
rcw said:
I guess that I did not read that article. The circular arc is what Peavy and JBL use, not through any mathematical considerations, but because it is so simple and matchs the OS very closely. I would expect the two devices to yield similar results because the profiles are so similar.
I fail to understand what a Laplace Equation has to do with the problem, but maybe thats because I did not read the paper. Could you send it to me? Maybe the points that you are trying to make will make more sense to me then, because they are not at all obvious at the moment.
I think this is the waveguide article Robert is referring to.
http://sound.westhost.com/articles/waveguides1.htm
http://sound.westhost.com/articles/waveguides1.htm