Hello,
http://www.diyaudio.com/forums/attachment.php?s=&postid=1789598&stamp=1238488590
first derivative on left hand,
second derivative on right hand.
Best regards from Paris, France
Jean-Michel Le Cléac'h
http://www.diyaudio.com/forums/attachment.php?s=&postid=1789598&stamp=1238488590
first derivative on left hand,
second derivative on right hand.
Best regards from Paris, France
Jean-Michel Le Cléac'h
gedlee said:
rcw said:
That study doesn't hold water. A change in the high pass crossover frequency for the horns in the “test” would have completely changed the "subjective" results of the study. It proves nothing than their setup will result in a certain perception among listeners. Regardless the horn or waveguide profile used, the closer to the acoustical cutoff a horn/waveguide is used, the more coloration is present. I would like to see what the listening results would have been for an 18” OS waveguide high passed at 1KHz. I sincerely doubt the listeners could have “detected” it as being a waveguide. I’ve got no argument with you other statements.
Rgs, JLH
pos said:
What about the smith horn, aka "diffraction horn"? 😀
JBL 2397 :
An externally hosted image should be here but it was not working when we last tested it.
IME, one of the worst devices ever created to torture the human ear. At least the wooden ones were useful as kindling for the fireplace.
I only get that result for an o.s. device that has a finite throat radius. If you start at the origin then the a^2 term disappears and for a 90 degree device the tan is 1 and the second derivative zero.
rcw.
rcw.
Hello,
What we are looking for is the derivative versus the curvilinear distance along the wall from throat. The derivative along the axial distance is pretty much useless.
A horn having a parabolic profile will not possess a constant second derivative.
Best regards from Paris, France
Jean-Michel Le Cléac'h
What we are looking for is the derivative versus the curvilinear distance along the wall from throat. The derivative along the axial distance is pretty much useless.
A horn having a parabolic profile will not possess a constant second derivative.
Best regards from Paris, France
Jean-Michel Le Cléac'h
Jmmlc said:
Hi ...
The two devices are not solving the same problem.
Jmmlc said:
This is incorrect. It IS the derivative WRT the axis since thats how the coordinates are defined. RCW is correct here.
Hello Earl,
You said:
"This is incorrect. It IS the derivative WRT the axis since thats how the coordinates are defined. RCW is correct here."
As waves drag along the wall while staying perpendicular to the wall, that's very doubtful.
Even it seems that is contradictory to your own use of a curved mouth ending à 90 degrees from the axis.
Best regards from Paris, France.
Jean-Michel Le Cléac'h
You said:
"This is incorrect. It IS the derivative WRT the axis since thats how the coordinates are defined. RCW is correct here."
As waves drag along the wall while staying perpendicular to the wall, that's very doubtful.
Even it seems that is contradictory to your own use of a curved mouth ending à 90 degrees from the axis.
Best regards from Paris, France.
Jean-Michel Le Cléac'h
If you remove the a^2 term the wall contour is not correct so it must be: 1*a^2.
To make the curve start at the origin you then can put it in the form f(x)-1, taking the second derivative gives the result that Jmmlc gets.
Rcw.
To make the curve start at the origin you then can put it in the form f(x)-1, taking the second derivative gives the result that Jmmlc gets.
Rcw.
Jmmlc said:
Hi ...
You are talking about boundary layer effects, small, but present, however, these are never considered, even in your designs. The assumption of a wave front moving parallel to the wall is the only rational one and reasonably accurate.
rcw said:
Sorry, but I don't follow. The wavefront curvature is accounted for in the wave equation.
What I am saying is that if you put the wall contour function as..
Y=(a^2+tan^2(b/2)x^2)^½
Then to look at the case where the throat has no area, i.e. just the wall contour alone then the a^2 cannot disappear or you get the square root of a constant times a square as an answer, a straight line.
So to get the correct contour, and a curve that starts at the origin, the value of “a” must be set at a constant that is subsequently subtracted from the expression to get a curve that starts at the origin, one is convenient for this, so twice diffentiating this gives…
1/(1+x^2)^3/2
This is the result that Jmmlc gives.
The area expansion expression has a constant, i.e. zero second derivative, but the wall contour expression only has one if we put a^2=0, in this case the wall contour is then not correct.
Overall the wall contour does not have a constant second derivative but the area expansion does.
Rcw.
Y=(a^2+tan^2(b/2)x^2)^½
Then to look at the case where the throat has no area, i.e. just the wall contour alone then the a^2 cannot disappear or you get the square root of a constant times a square as an answer, a straight line.
So to get the correct contour, and a curve that starts at the origin, the value of “a” must be set at a constant that is subsequently subtracted from the expression to get a curve that starts at the origin, one is convenient for this, so twice diffentiating this gives…
1/(1+x^2)^3/2
This is the result that Jmmlc gives.
The area expansion expression has a constant, i.e. zero second derivative, but the wall contour expression only has one if we put a^2=0, in this case the wall contour is then not correct.
Overall the wall contour does not have a constant second derivative but the area expansion does.
Rcw.
RCW
Sorry, I still don't get the point. The slope is as you state and the second derivative is just the drivative of that. No its not constant but its not what Jean-Michael claims either. I don't get the need to do all the twisting of the equations to suite some need to make it look worse.
If you want to talk about the slope change as seen by the wavefront, well that's another thing altogether. Only the waveguide approach of using the full wave equation can give you that, simply because you can't just assume that the wavefront will follow the contour and with Webster's approch you don't really know what the wavefront is so its not possible to calculate the slope change relative to that wavefront.
No matter how you try and twist things arround it all comes back to either you use the waveguide approach or you are just guessing.
Sorry, I still don't get the point. The slope is as you state and the second derivative is just the drivative of that. No its not constant but its not what Jean-Michael claims either. I don't get the need to do all the twisting of the equations to suite some need to make it look worse.
If you want to talk about the slope change as seen by the wavefront, well that's another thing altogether. Only the waveguide approach of using the full wave equation can give you that, simply because you can't just assume that the wavefront will follow the contour and with Webster's approch you don't really know what the wavefront is so its not possible to calculate the slope change relative to that wavefront.
No matter how you try and twist things arround it all comes back to either you use the waveguide approach or you are just guessing.
The point that I am making is that you stated that the wall contour curve that minimises diffraction has a constant second derivative. And the o.s. curve does not have one but the area expansion of the o.s. waveguide does.
That would mean that either the o.s. curve does not minimise diffraction or it is the second derivative of the area expansion that does.
Other than that maybe the second derivative of the wall contour is constant in o.s. coordinates but not in Cartesian ones.
The two graphs that Jmmlc posted give the first and second derivatives, I.e.
d/dx(f(x)), and this again differentiated, in Cartesian coordinates.
What I am wondering is his interpretation of what you mean by the constant second derivative the correct one, or must the wall curve be differentiated with repect to something else?
Rcw.
That would mean that either the o.s. curve does not minimise diffraction or it is the second derivative of the area expansion that does.
Other than that maybe the second derivative of the wall contour is constant in o.s. coordinates but not in Cartesian ones.
The two graphs that Jmmlc posted give the first and second derivatives, I.e.
d/dx(f(x)), and this again differentiated, in Cartesian coordinates.
What I am wondering is his interpretation of what you mean by the constant second derivative the correct one, or must the wall curve be differentiated with repect to something else?
Rcw.
RCW
I understand now. There is no curve that has zero second derivative except a straight line.
I am not really sure what the correct interpretation is only that when the full wave equation is used you get the diffraction as a result. With any other aproach you don't know what the wavefront is so you can't calculate the diffraction. Remember that difraction in a smooth contour waveguide was an entirely new result that came out of the use of the wave equation approach. It was not predicted by Webster and hence was not considered. Going back and trying to "fix" Webster to calculate the diffraction does not seem workable to me.
When you calculate the area change that is relative to the axis and not the wavefront correct?
I understand now. There is no curve that has zero second derivative except a straight line.
I am not really sure what the correct interpretation is only that when the full wave equation is used you get the diffraction as a result. With any other aproach you don't know what the wavefront is so you can't calculate the diffraction. Remember that difraction in a smooth contour waveguide was an entirely new result that came out of the use of the wave equation approach. It was not predicted by Webster and hence was not considered. Going back and trying to "fix" Webster to calculate the diffraction does not seem workable to me.
When you calculate the area change that is relative to the axis and not the wavefront correct?
Why does everyone want to make this so difficult?
For minimum diffraction from waveguide walls, there should be zero second derivative of the walls, or straight sides, which equates to a conical waveguide.
However, as Earl has pointed out, a spherical wavefront must be applied to the throat of a conical waveguide from the source to meet his objectives.
There being only planar wavefront sources, curved sides have to be used to morph the planar wavefront of a driver at the throat into a spherical wavefront as the wavefront approaches the conical asymptotes of the waveguide. For a wall curved to have the smoothest transition to minimize diffraction (HOMS) from the throat to the conical asymptote, it has to have the minimum second dervative (or CHANGE in slope) possible, that being the OS curvature.
For minimum diffraction from waveguide walls, there should be zero second derivative of the walls, or straight sides, which equates to a conical waveguide.
However, as Earl has pointed out, a spherical wavefront must be applied to the throat of a conical waveguide from the source to meet his objectives.
There being only planar wavefront sources, curved sides have to be used to morph the planar wavefront of a driver at the throat into a spherical wavefront as the wavefront approaches the conical asymptotes of the waveguide. For a wall curved to have the smoothest transition to minimize diffraction (HOMS) from the throat to the conical asymptote, it has to have the minimum second dervative (or CHANGE in slope) possible, that being the OS curvature.
Pooge
Thanks - thats completely correct and I agree that some people seem to want to complicate the situation - makes spinning a story that much easier I guess. The detailed math of the OS waveguide is very complex, but when its all done, the rational for it is really pretty straightforward.
Thanks - thats completely correct and I agree that some people seem to want to complicate the situation - makes spinning a story that much easier I guess. The detailed math of the OS waveguide is very complex, but when its all done, the rational for it is really pretty straightforward.
The complicated part is how to get a plane wave for all frequencies covered by the waveguide. I do not think it's possible.😉pooge said:
soongsc said:
Nothing is perfect. The job of an engineer is to make the best choices possible under the circumstances.
gedlee said:
For that part of the wave front close to the boundary – yes! Nothing else Jean-Michel is praying.
rcw said:
!!
gedlee said:
WOW 😉 sometimes even the obvious has to be stated ..
As I said elsewhere - only *infinite* duct and *infinite* conical hold that assumption – both of which far form being "real world" horns – no? 😀
pooge said:
No – there is *always* diffraction for the transition part of the OS (simplified for where the wave front is bent the most)
It is not said that Earls optimisation is the best with respect to the sonic outcome as he failed to scientifically link his math to listening tests – and what the above mentioned paper is worth, well .....
Also Earl isn't clear about wave fronts and sound fields in a deeper understanding as he has demonstrated recently.
Pretty disappointing for someone who has studied the topic the better part of his life
# (edited – as got wrong)
If we only look at the summed second derivative "the difference of boundary angles" we end up with the *same* diffraction for *any* transition form planar wave front to a horn contour with a certain included angle.
And *if* the transition to a certain included angle already is performed – you *have to* do the transition to 2Pi or 4Pi space finally. Earl cuts that out of discussion deliberately.
Bottom line - Earls arguments related to "diffraction" are for the bin – mathematically or scientifically seen – or from which ever point of view you look at the topic ....
Only judgement IMO is the sound field created and – of course - the limitations in band width due to the irregularity occurring at the top end due to throat dimension – as this is a severe restriction to usability too.
Here we only have very few data – Bjorg Kolbrek's BEM simus some time back – maybe not enough to really judge
Michael
mige0 said:
You are one of the people complicating things by twisting people's words.
I did not say there was NO diffraction. Earl did not say there is NO diffraction. That's why he uses foam.
I said MINIMIZE the diffraction.
Until you have irrefutable proof of linking the math to the sonic result, you should not be accusing others for any "failure" of the same.
pooge said:
As I said – diffraction isn't minimised by OS as the "bending" of the wave front is the same for any transition to a certain included angle.
*I* don't have to do the prove for Earl's claims – he has to do by himself as it's *his* claim that diffraction is minimised by OS – which isn't – in its outcome – IMO.
Why do you think is foam so important for OS if any other horn does without ?
And no - I'm not twisting words of others - I express with my own ones!
Michael