Is thee a constraint on how the length of the transition from the OS to conical?
Slope change and its ill effects would be lowered if this part were lengthened, though of course that would lengthen the WG.
Slope change and its ill effects would be lowered if this part were lengthened, though of course that would lengthen the WG.
noah katz said:
As Earl said, there isn't a transition to conical although it looks that way. The only inputs to the OS equation are throat diameter, initial throat angle and coverage angle. From there, you just plug in the Z (depth) number and calculate the diameter at that depth from the equation. A 20" deep waveguide will have the same shape as a 10" deep waveguide for the first 10" of its depth, if they both have the same three inputs.
I see, thanks.
I wonder what would happen then if you spliced two OS's together, one of them having the section near the throat scaled up axially to reduce slope rate of change.
I wonder what would happen then if you spliced two OS's together, one of them having the section near the throat scaled up axially to reduce slope rate of change.
noah katz said:
I think the term "ill effects" (of diffraction) is someting to question more deeply and generally.
Simply - diffraction can't be avouded in real (accoustic) life - especially not with horns.
So we should not see diffraction as our "enemy" as it also can be utilized - or at least handled - its a simple law of physics - no bad will.
In this farme we have to ask what exactly is the optimisation the oblade spheroide contour provides?
The term "lowest HOM possible" has to be translated - and in my understanding the only translation that makes some sense is the translation into "how much impact does diffraction have into the raggedness (swiss cheese defects) of a soundfiled.
I might be wrong - though....
If we look at the idea of stretching the initial transition part of an OS contour to get "less ill effects" - I'm not sure how to judge the benefits if not related to soundfield analysis or distrotion analysis (due to second order effects as outlined).
Maybe we would come to the result that oblade spheroide is just *one* way to achieve the goal - probably the most economic one - meaning the quickest transition possible at comparable "swiss cheese defects" - who knows?
*I* haven't analysed Earls math and what ancillary conditions he assumed for solution - and I don't plan to dive into this either - thats for sure.
Michael
catapult said:
No, it *is* a transition to conical - with conical happening asymptotically (meaning never ever in its very sense)– nevertheless a "transition to conical"
It's just not the way that you have a "pure" transition part joining a "pure" conical part
😉
Michael
mige0 said:
The point is a single OS equation determines the whole curve (out to the point where the mouth round-over starts.) There's no OS equation to build the throat transitioning to a conical equation to build the body.
Jack Bouska points out that delaying the transition to conical lowers the frequency where the horn loses CD on the high end. So, everything else being equal, you wan't to get it done as fast as you can to preserve good off-axis HF response. Of course everything else is never equal. 😉
If you look at the junction between a straight pipe and a conical horn all the wavefront bending occurs at the junction of these two.
This is known as a scattering junction and the amount of scattering is proportional to the difference in area between the incident and scattered wave, and diffraction is proportional to the square of the scattering amplitude.
If we now bend our wave with two scattering junctions then the wave front is still the same but now the diffraction is half of the previous case.
If we now consider a smooth curve the curve that has the same notional scattering at every point from where the incoming plane wave to the final wavefront we want is found, results in the same wavefront as the first case we considered but minimises the amount of diffraction.
The wall contour of the o.s. waveguide is this shape.
Rcw.
This is known as a scattering junction and the amount of scattering is proportional to the difference in area between the incident and scattered wave, and diffraction is proportional to the square of the scattering amplitude.
If we now bend our wave with two scattering junctions then the wave front is still the same but now the diffraction is half of the previous case.
If we now consider a smooth curve the curve that has the same notional scattering at every point from where the incoming plane wave to the final wavefront we want is found, results in the same wavefront as the first case we considered but minimises the amount of diffraction.
The wall contour of the o.s. waveguide is this shape.
Rcw.
If you allow for a small error, one can extend the OS shape as pure conical at at point "far away" from the throat, as Michael has pointed out. Using the spreadsheets (I have JoshK's and John Kreskovsky's) one can see that the contour error is really small and certainly neglectable in practise.
- Klaus
- Klaus
rcw said:
This part is absolutely clear to me.
rcw said:
This part too.
rcw said:
But what exactly means:
" the difference in area between the incident and scattered wave "
?
Michael
catapult said:
Good to know such easy rules of thumb, thanks
Would be interesting if he also says that diffraction basically is the *same* as is "the difference in area between the incident and scattered wave" - just stretched a little bit?
Michael
gedlee said:
Wouldn't a quad-spheroidal waveguide solve a lot of problems then?
Picture something like this, but with an oblate spheroidal contour:
An externally hosted image should be here but it was not working when we last tested it.
A device like this should offer the following benefits:
#1 - Instead of a single waveguide with ninety degree coverage, four waveguides with 22.5 degree coverage coupled together will have lower diffraction, as the transition from the throat of the compression driver to the final 22.5 degree waveguide is a gentler transition than what is possible in a 90 degree waveguide.
#2 - By using an elliptical mouth for each waveguide, you eliminate the on-axis response hole
#3 - You could reduce the vertical coverage angle and reduce the off-axis lobes
It wouldn't be easy to build, but it offers some benefits over a conventional waveguide, without any obvious drawbacks.
Some might think that segmenting the throat would create diffreaction, but I believe that is only a concern when the dimensions are sufficiently large. For instance, if the gap between each segment is less than 1/4", it will be acoustically invisible.
If anyone wants to mess with diffraction in real-time, check this out:
http://www.ngsir.netfirms.com/englishhtm/Diffraction.htm
http://www.ngsir.netfirms.com/englishhtm/Diffraction.htm
An externally hosted image should be here but it was not working when we last tested it.
In the parallel tube section if the wavefront is flat the wave is said to be a one parameter wave, i.e. it has only one mode.
If we consider the junction to the conical horn as a waveguide then the wavefront must be such that a normal to the wall at that point is tangent to it, an ideal one parameter wave in a conical horn is an exact spherical cap.
As a first approximation if we take the difference between the flat disc at this point, (that would be in the tube), and the spherical cap at this point, (that would be in the conical horn), this is the amount of scattering that has occurred, this being a simple measure of the wavefront curvature at this point.
It is not accurate to say that diffraction is the same as the difference between the incident and scattered wave, because as I have said, the difference in curvature of the wavefront is the measure of scattering whereas the geometry of the scatterers is the measure of diffraction.
From this all wavefronts that are transformed from on curvature to another have the same total scattering and the diffraction associated with it is maximum if all scattering occurs at one point.
Rcw.
If we consider the junction to the conical horn as a waveguide then the wavefront must be such that a normal to the wall at that point is tangent to it, an ideal one parameter wave in a conical horn is an exact spherical cap.
As a first approximation if we take the difference between the flat disc at this point, (that would be in the tube), and the spherical cap at this point, (that would be in the conical horn), this is the amount of scattering that has occurred, this being a simple measure of the wavefront curvature at this point.
It is not accurate to say that diffraction is the same as the difference between the incident and scattered wave, because as I have said, the difference in curvature of the wavefront is the measure of scattering whereas the geometry of the scatterers is the measure of diffraction.
From this all wavefronts that are transformed from on curvature to another have the same total scattering and the diffraction associated with it is maximum if all scattering occurs at one point.
Rcw.
noah katz said:
RCW
Not sure that people will follow all that you said but this last sentence is the key. Find that curve that spreads the diffraction over as large an distance as possible, thus minimizing it! Wait, Wait, I know that one!
I really don't understand all the "what if" questions. We have what we have and we know what we want. Hence it seems pretty clear to me that taking "what we have" - a flat planar wave in a circular aperature - and "making what we want" - a spherical wave of an extent larger than a wavelength", but with a slow edge transition to zero rather an abrupt one (reduces reflection and dffraction) - would meet the design criteria. That, coincidentally, is exactly what an OS waveguide does.
Now, we can hypothesize about the goals (a spherical wave of an extent larger than a wavelength?), but I don't think that would yield much difference from what I have stated, or we can discuss the options for the source, like a square as opposed to a circle?, but none of this is new.
Patrick Bateman said:
Thanks, Patric - thats a good one too.
If you take the diffraction around the corner
http://www.ngsir.netfirms.com/englishhtm/Diffraction3.htm
you see what I was outlining earlier to correct for Earls statement:
mige0 said:
Michael
rcw said:
This part is absolutely clear to me.
rcw said:
This part too.
Can you some further elaborate on "the geometry of the scatters" ?
rcw said:
Here you tell us that all that counts *for the wave front* is the "total amount of wave front bending" in the end – but it does not tell us about the "established sound field" damages.
Or have I missed something – possibly the relationship between magnitude of diffraction and the magnitude of the second source created?
The point I would like to highlight is that its beneficial to a better understanding that there are two things to keep apart IMO.
1.) the impacts of diffraction at the "shape of the wave front" and
2.) the impacts of diffraction on the "established sound field"
point one is about the time of arrival
point two is about frequency response at a certain point in space due to interference
Michael
It is true that the actual wavefront in our example is not transformed into a spherical cap at the junction because of the presence of diffraction.
The actual isophase surface produced depends upon the frequency because scattering varies as the wave number of the incident wave.
The point is that if the scattering occurs at a set of points on a smooth curve rather than suddenly at a single point we get something that much more resembles a true spherical cap for a wavefront and the closer it is to this the lesser the presence of higher order modes caused by diffraction, because the wavefront shape is distorted due to the reinforcement/cancellation effects of the modes produced by diffraction.
The geometry of the scattering points requires that the scattering at every point along the wall curve is the same since the total diffraction is the sum of the squares of these points and the sum is minimum if the scattering at each point is identical and spread over the longest length obtainable , such wall curves have a constant second derivative.
The nature of the field produced can be deduced from the length of the tangent to the wall at a point on the wall to where it crosses the horn axis.
If this has a “kr” number is much less than one then the sound field at that frequency is dominated by the imaginary part of the impedance and any modes that exist are evanescent and will not radiate bellow the local cut off frequency.
Rcw.
The actual isophase surface produced depends upon the frequency because scattering varies as the wave number of the incident wave.
The point is that if the scattering occurs at a set of points on a smooth curve rather than suddenly at a single point we get something that much more resembles a true spherical cap for a wavefront and the closer it is to this the lesser the presence of higher order modes caused by diffraction, because the wavefront shape is distorted due to the reinforcement/cancellation effects of the modes produced by diffraction.
The geometry of the scattering points requires that the scattering at every point along the wall curve is the same since the total diffraction is the sum of the squares of these points and the sum is minimum if the scattering at each point is identical and spread over the longest length obtainable , such wall curves have a constant second derivative.
The nature of the field produced can be deduced from the length of the tangent to the wall at a point on the wall to where it crosses the horn axis.
If this has a “kr” number is much less than one then the sound field at that frequency is dominated by the imaginary part of the impedance and any modes that exist are evanescent and will not radiate bellow the local cut off frequency.
Rcw.
rcw said:
This part is absolutely clear to me.
In fact – wavefront never gets transformed into a spherical ever – its asymptotically as is the OS contour itself – and even if you use any other contour or just a " scattering junction " – spherical will occur with any of this transitions - but only at infinity.
So the question remains what *exactly* is the benefit of OS – doing the transition the quickest (at least the most part of the transition to be more precise)?
rcw said:
This part too is clear to me - at least where you conclude a "constant second derivative " is a requirement for the solution we / Earl are after here (not yet in agreement that that solution is the best compromise ever, though – which is a completely different topic I don't want to mix in right now).
But again - what actually is " The geometry of the scattering points " ?
Michael
rcw said:
No - this we have been through in length (we are still awaiting Earl's concession speach though 😉 ).
Scroll back a view pages or have a look at my paper (http://www.kinotechnik.edis.at/pages/diyaudio/DDCD/DDCD_dipole_horn.html Chapter "In the Light of Ancient versus Nowadays Knowledge") which basically is a summary of my thoughts about the topic developed through the course of many posting here and elsewhere.
Michael