Go Back   Home > Forums > >
Home Forums Rules Articles diyAudio Store Blogs Gallery Wiki Register Donations FAQ Calendar Search Today's Posts Mark Forums Read

Multi-Way Conventional loudspeakers with crossovers

Jean Michel  on LeCleac'h  horns
Jean Michel  on LeCleac'h  horns
Please consider donating to help us continue to serve you.

Ads on/off / Custom Title / More PMs / More album space / Advanced printing & mass image saving
Reply
 
Thread Tools Search this Thread
Old 31st July 2009, 01:08 AM   #431
rcw is offline rcw  Australia
diyAudio Member
 
Join Date: Jul 2005
Location: sydney nsw
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.
  Reply With Quote
Old 31st July 2009, 02:41 PM   #432
gedlee is offline gedlee  United States
diyAudio Member
 
gedlee's Avatar
 
Join Date: Dec 2004
Location: Novi, Michigan
Your physics traioning and mine are quite different as I have never seen any of the things which you refer to. Everyone that I know of in Acoustics use the standard techniques that I use. I've asked you to write your approach down somewhere, but that doesn't seem to have happened.
__________________
Earl Geddes Gedlee Website
  Reply With Quote
Old 1st August 2009, 07:35 AM   #433
rcw is offline rcw  Australia
diyAudio Member
 
Join Date: Jul 2005
Location: sydney nsw
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.
  Reply With Quote
Old 1st August 2009, 05:19 PM   #434
gedlee is offline gedlee  United States
diyAudio Member
 
gedlee's Avatar
 
Join Date: Dec 2004
Location: Novi, Michigan
Quote:
Originally posted by 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.
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.
__________________
Earl Geddes Gedlee Website
  Reply With Quote
Old 1st August 2009, 05:24 PM   #435
mige0 is offline mige0  Austria
diyAudio Member
 
mige0's Avatar
 
Join Date: Jan 2005
Location: Austria, at a beautiful place right in the heart of the Alps.
Quote:
Originally posted by 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.

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!


Quote:
Originally posted by rcw

...
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
  Reply With Quote
Old 2nd August 2009, 01:55 AM   #436
rcw is offline rcw  Australia
diyAudio Member
 
Join Date: Jul 2005
Location: sydney nsw
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.
  Reply With Quote
Old 2nd August 2009, 02:16 AM   #437
KSTR is offline KSTR  Germany
diyAudio Member
 
KSTR's Avatar
 
Join Date: Jul 2007
Location: Central Berlin, Germany
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
  Reply With Quote
Old 2nd August 2009, 04:04 AM   #438
Ed LaFontaine is offline Ed LaFontaine  United States
diyAudio Member
 
Ed LaFontaine's Avatar
 
Join Date: Feb 2004
Location: where the Appalachians rise from the Blue Grass
...or that "constant directivity" for the OS waveguide is a misnomer?...due to the "hole in the middle"?
  Reply With Quote
Old 2nd August 2009, 08:45 AM   #439
mige0 is offline mige0  Austria
diyAudio Member
 
mige0's Avatar
 
Join Date: Jan 2005
Location: Austria, at a beautiful place right in the heart of the Alps.
Quote:
Originally posted by rcw
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.


Quote:
Originally posted by rcw

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?


Click the image to open in full size.
taken from: http://en.wikipedia.org/wiki/Gaussian_function
Carl Friedrich Gauss: http://en.wikipedia.org/wiki/Carl_Friedrich_Gauss


Quote:
Originally posted by rcw


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 !


Quote:
Originally posted by rcw


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".


Quote:
Originally posted by rcw


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??

Quote:
Originally posted by rcw


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
  Reply With Quote
Old 2nd August 2009, 08:46 PM   #440
rcw is offline rcw  Australia
diyAudio Member
 
Join Date: Jul 2005
Location: sydney nsw
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.
  Reply With Quote

Reply


Jean Michel  on LeCleac'h  hornsHide this!Advertise here!
Thread Tools Search this Thread
Search this Thread:

Advanced Search

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off

Forum Jump


New To Site? Need Help?

All times are GMT. The time now is 11:36 AM.


Search Engine Optimisation provided by DragonByte SEO (Pro) - vBulletin Mods & Addons Copyright © 2018 DragonByte Technologies Ltd.
Resources saved on this page: MySQL 15.00%
vBulletin Optimisation provided by vB Optimise (Pro) - vBulletin Mods & Addons Copyright © 2018 DragonByte Technologies Ltd.
Copyright ©1999-2018 diyAudio
Wiki