Jean Michel on LeCleac'h horns

KSTR said:
Michael,

Care to show us the OS version *with* roundover into the baffle? Otherwise this again is sort of unfair.

And please normalize the directivity plots to the 0° on-axis SPL (only a few mouse clicks away, "normalize --> to curve in x-graph"). EDIT: Then again, we know that 0° not necessarily is the optimum angle, for OS....

- Klaus

Normailizeing the OS to the axis makes things look far worse than they really are. Thats because a small hole right on axis becomes a huge off-axis peak. There really isn't simple solution.
 
I have been playing about with the Axisdriver software and these plots might be of interest.
The first shows a comparison of a spherical and plain conical horn at two frequencies...

sphconcomp.jpg


The spherical shows a smooth pattern whereas the conical is rougher.

The next plots are taken at11.247kHz. where they both show an on axis hole.
The spherical one is a smooth one that is a good approximation to ideal, whilst the conical is very rough and complex.


11kcomp.jpg


Although both horns show a similar anomaly the spherical one has a far neater pattern than the conical.
The spherical reverts to a close resemblance to a Gausian type cross section above this frequency, whereas the conical pattern is very confused and complex.
rcw
 
Thanks for your reactions.
Earl - special thanks for *not* posting "it's just another bunch of pretty pictures" or something like - very much appreciated.

As for the "demands" to also show in more detail this and that – yes I know there is a *lot more* we would like to see and haven't yet.
It really makes me happy that there is so much interest in what I presented – but as said – it's a considerable effort to set up simulations in all the variants we would have interest in and run them in as much detail as we would actually need.

On the other hand its more about "showing the answers by looking out for the questions" anyway – meaning by comparing the few pix I have posted we already and pretty easily can state most of the core design goals for "diffraction aligned horns".

So its kind of curriculum I work through to efficiently optimise insight "in general" combined with what I'm mostly interested in for further developing and refining on my min phase DiHo (the "whale" of my first posting not yet built).

:)



Michael
 
Hello,

ScottG said:
It's more than diffraction at the mouth with regard to reflections and what they *superimpose* on the output.

Yes, there is the refflection inside the horn, too.

According to my experimental device for measuring the horn reflection's we see in the picture below that there are multiple sources of reflections:

An externally hosted image should be here but it was not working when we last tested it.


Red: just a tube.
Orange: RCF HF101
Blue: JBL 2345

Why multiple? Because this firsts echos have a ripple response (who cause a comb filtering due to its delays).
Two sources of reflection for the RCF (sinusoid curve) and a least 3 for JBL ("quasi-chaotic curve"), especially visible between 2Khz and 4Khz.

The tube have a ripple response too, I think it comes from the compression itself or its acoustic adaparation with the tube.
 
A more correct term for the field is a scattering field as this includes the diffraction and the reflection from the impedance anomaly at the mouth.
The value of this description is that it makes clear that the minimum reflection is also the minimum diffraction.

What we want ideally is a transition to "pure diffusion", in which all scattering is forward and divergent, (diffraction is scattering off boundaries), and the ideal beam has a Gausian envelope.
rcw.
 
rcw said:

What we want ideally is a transition to "pure diffusion", in which all scattering is forward and divergent, (diffraction is scattering off boundaries), and the ideal beam has a Gausian envelope.
rcw.

I'm not sure that I agree with the terminology of "diffusion" - that term means something different to me, sound waves don't "diffuse" they propagate - but the part about the Gaussian is correct.

Since the far field radiation pattern can be shown to be a transform pair with the mouth velocity distribution it's interesting to look at the characteristics of these "pairs". The Gaussian shape turns out to transform into another Gaussian properly scaled. This means that a Gaussian mouth velocity distribution will yield a Gaussian polar response. (I assume thats whats meant by "Gausian envelope".)
 
That's what I mean Earl the the envelope is just a reference to an intensity variation so many standard deviations wide.

The references to scattering and diffusion come about because in essence the wave theory of sound is a statistical description of the behavior of a large assemblage of elastic particles.

Diffusion is where these particles only scatter off themselves and not any kind of obstacle or boundary, analogous to a wave propagating in “free” air. I find this description useful because the solutions to the diffusion equation are Gaussian functions.

Being a spherical wave the wavefront has a component normal to the duct wall, and it is the scattering of this component off the duct wall that causes a diffraction field that spoils the formation of a Gaussian velocity distribution at the mouth.
Rcw.
 
rcw said:
Diffusion is where these particles only scatter off themselves and not any kind of obstacle or boundary, analogous to a wave propagating in “free” air. I find this description useful because the solutions to the diffusion equation are Gaussian functions.
Rcw.

I have to disagree with you here. The Diffusion Equation does not have a term that accounts for inertia (its first order not secodn) and hence diffusion has no inertia while waves and the wave equation does. Sound pressure changes do not 'diffuse" through a gas they move as waves which REQUIRES an inertia term.

There can be "wave like" solutions in a diffusion medium, but only if there is a sinusoidal forcing function. And things like reflection don't happen in diffusion because of the lack of inertia. Another way to look at it is the diffusion equation only has real exponential solutions, it can't have complex ones.
 
While what you say about the diffusion equation is certainly true it is never the less a useful generalisation.

This is because it has a solution that is a functional returned by the Euler Lagrange equation.

Since both this and the diffusion equation are first order in time you are able to change the time dependance to a space one.

This is consistent because the equations of motion now become least action path integrals in accordance with Hamilton's principle.

This has in effect turned the problem into one amenable to analysis by various topology and mapping theories. For instance the beam envelope is ideally a minimum surface, and this can be parametised as a stationary point problem by the use of the E-L equation.
Rcw.
 
I imagine Earl that our approaches differ because the only background I have in acoustics is via seismology and thence seismic tomography.

I make no claim for originality for such an approach as seismic tomographers in our turn borrowed these types of formulations from quantum and relativistic mechanists, and can be found in the extensive literature on these subjects, as well as these applied to such things as tomography.
Rcw.
 
rcw said:
I imagine Earl that our approaches differ because the only background I have in acoustics is via seismology and thence seismic tomography.

I make no claim for originality for such an approach as seismic tomographers in our turn borrowed these types of formulations from quantum and relativistic mechanists, and can be found in the extensive literature on these subjects, as well as these applied to such things as tomography.
Rcw.

The problem that I have is that you keep claiming techniques that to me won't work and then when I ask for the mathematical support you never seem to come through. I can see how your potential theory will work for low frequencies where the wave equation converges on the difusion equation at these frequencies, but to my knowledge such a technique is not possible at small wavenumbers since the solutions of the two approaches are quite different.

My sole background is acoustics, and I have not seen anyone claim what you are claiming in my field.
 
rcw said:
I imagine Earl that our approaches differ because the only background I have in acoustics is via seismology and thence seismic tomography.

I make no claim for originality for such an approach as seismic tomographers in our turn borrowed these types of formulations from quantum and relativistic mechanists, and can be found in the extensive literature on these subjects, as well as these applied to such things as tomography.
Rcw.


Most interesting – now I better understand.
I guess in seismic science you simply *have to* look for more complex analogies for whats happening as you totally *have to* relay on theories of propagation, as you not simple can move the mic to whatever position you like.
Furthermore you have to deal with "bounderies" that are not as black and white as are with common loudspeaker horns (a lot of layers of different acoustic properties – completely hidden in the ground).


Very challenging!


rcw said:

...
What we want ideally is a transition to "pure diffusion", in which all scattering is forward and divergent, (diffraction is scattering off boundaries), and the ideal beam has a Gausian envelope.
rcw.


Probably I did't get you right but I have a feeling that what I mean with "diffraction aligned horns" (minimising ill effects of the complex of "diffraction > reflection > delay > interference") is what you describe here.

What is a beam with "Gausian envelope" actually in out context – could you please elaborate on that – if possible in a low level manner (I guess everybody already knows what a Gausian curve looks like form statistics)?

Michael
 
If you want mathematical support for the proposition that the solution to the wave and diffusion equations are synonymous for all wave numbers I cannot give it because there isn't any.

But that is not what I said, what I said was that this shows that our beam ideally has a Gaussian cross section, and we might test how close a given beam is to it by means of the calculus of variations.

For instance the beams produced by the Le Cleche horn look remarkably Gaussian at most frequencies but they are not of constant width at all frequencies, i.e. it is not a constant directivity device, the o.s. with suitable flared mouth produces a beam that has a good resemblance to a Gaussian one up to a frequency where it develops a hole in the middle, (the shallow circular arc device does the same thing).

From this it would seem that it is not possible to produce an axis symmetric device that produces an approach to an ideal beam at all frequencies and also has constant directivity.

It would be nice to know if this is true or not, and this is a method that might be useful in finding out.

Simply put Micheal the Gausian beam is one that is a divergent beam that has no diffraction causing it to spread.
If the beam has such a velocity distribution across it at the horn mouth, then this will continue out into the room unchanged.
The envelope is simply defining that the boundary of the beam is somewhere, in audio it is usual to specify where it is 6db. Down.
The envelope has what is known as a minimum surface, this is one that has zero average curvature there is only one curve of revolution that has this property, that is the catenoid of revolution, and this is the envelope of a Gaussian beam.
Rcw.
 
rcw,

does this boil down to the end user to the following notion:

In a listening environment with little reflection and fixed sweet spot the LC contour is better, while with a more reverberant space and/or wider listening sweet-spot the OS might be better, as an overall compromise?

- Klaus
 
rcw said:
If you want mathematical support for the proposition that the solution to the wave and diffusion equations are synonymous for all wave numbers I cannot give it because there isn't any.

Rcw.

BEWARE !
Its usually JohnK and Earl that are the math magicians here - certainly not me.
:D

rcw said:

But that is not what I said, what I said was that this shows that our beam ideally has a Gaussian cross section, and we might test how close a given beam is to it by means of the calculus of variations.

For instance the beams produced by the Le Cleche horn look remarkably Gaussian at most frequencies but they are not of constant width at all frequencies, i.e. it is not a constant directivity device, the o.s. with suitable flared mouth produces a beam that has a good resemblance to a Gaussian one up to a frequency where it develops a hole in the middle, (the shallow circular arc device does the same thing).
Rcw.

Do you refer to a "Gaussian" shape we would get if we take a vertical slice out of the directivity sonograms shown – meaning the "SPL distribution at a certain frequency over angle" should look close to a Gaussian curve?


600px-Normal_distribution_pdf.svg.png

taken from: http://en.wikipedia.org/wiki/Gaussian_function
Carl Friedrich Gauss: http://en.wikipedia.org/wiki/Carl_Friedrich_Gauss


rcw said:


From this it would seem that it is not possible to produce an axis symmetric device that produces an approach to an ideal beam at all frequencies and also has constant directivity.

It would be nice to know if this is true or not, and this is a method that might be useful in finding out.

Rcw.

Agree - certainly it would be nice - actually revolutionary ! :D


rcw said:


Simply put Micheal the Gausian beam is one that is a divergent beam that has no diffraction causing it to spread.
If the beam has such a velocity distribution across it at the horn mouth, then this will continue out into the room unchanged.
Rcw.


This is a new idea (to me) to define "diffraction".


rcw said:


The envelope is simply defining that the boundary of the beam is somewhere, in audio it is usual to specify where it is 6db. Down.
Rcw.

Mmmhh??

rcw said:


The envelope has what is known as a minimum surface, this is one that has zero average curvature there is only one curve of revolution that has this property, that is the catenoid of revolution, and this is the envelope of a Gaussian beam.
Rcw.

Again - you refer to the envelope of "SPL over angle" to be "catenoid of revolution"?

Michael
 
Yes Klaus, that is certainly the sort of consideration I would have in mind if choosing between the different schemes.

The point is Micheal that the Gaussian beam has one maximum, whereas beams that have diffraction artifacts have “Airy”, type maxima and minima across them caused by interference.

In the sonogram the distribution should ideally be that of the Gaussian beam in polar coordinates, and a constant directivity device will show a set of parallel bands over a frequency range where it is c.d.

From what I have seen the sonogram of the LeCleche type horn produce a Very Gaussian like distribution at nearly all frequencies but it has the characteristic “fat whale”, shape, indicating that it is not c.d.: can we then make a horn that does both?

At the moment I don't know, and am looking at methods of finding out.

It seems Ed that there is a semantic issue to do with the definition of c.d. here.
And the speaker system in question probably does not have constant power responce above a certain frequency, and if you require this for your definition then by definition it is not.
Rcw.