Some of you guys may be interested in some simulation results I posted over on AA. They compare polar response and waterfall plots for a LeCleac'h horn to a conical horn with no round over at the mouth and no throat transition. This was because someone over there was claiming a straight conical horn was the greatest thing since sliced bread (my own synopsis). Of course he also happens to sell one. As I noted there, I found a comparable OS flair to be much more similar to the LeCleac'h than a straight conical. Here's the link:
http://www.audioasylum.com/forums/hug/messages/14/143151.html
http://www.audioasylum.com/forums/hug/messages/14/143151.html
John Sheerin said:
Nice work, although I would like to have seen the OS sims.
I won't go to AA because the moderators thrive on conflict and do nothing to minimize it, agravating it in fact. Thats fine is your just a lurker, but its a disaster if you are someone with a profile. You becomne a real target. Things get bad here sometimes, but nothing like over there.
panomaniac said:
To give a teaser what powerful tool BEM can be I'd like to show two preliminary simus I've run by AxiDriver.
The two horn contours simulated are almost identical but for one the throat angle does not fit for the plain wave front injected.
fig 1
fig2
This form of visualisation is not very often used around here so I'd possibly first introduce what we actually can see in such plots.
Basically these form of plots focus on getting a intuitively handle on the subject of directivity.
The directivity is shown at a certain distance from the driver (in our case 5m / 30 feet of "mic" distance). directivity varies with distance for all but very few exceptions – but variations are *usually* not that big that we have to do more than a sanity check once and then (in fact it would be a interesting topic of its own to dive into in more detail).
From left to right we see SPL over frequency – exactly the same way as in a frequency response plot everybody is familiar with despite that SPL *level* is coded in colours instead of y-axis height - "hot"-red for high SPL / "cold"-blue for low SPL in our case – corresponding to the SPL coding bar to the right.
This is true for *any* horizontal line you follow in the graph – no colour change = ruler flat FR.
Obviously the horizontal line in the middle of the graph represents SPL variations over frequency for on-axis measurements whereas any horizontal lines above and below represent FR traces at certain off-axis angels.
So now - *if * we would have a ideal omni speaker we would see no colour change whatsoever over the whole graph – as there, by definition, is the same ideal FR at all room angles.
*If* we would have a ideal constant directivity speaker (one with a certain directivity) we would see no colour changes along the horizontal lines but colour changes in the vertical direction – giving the impression of looking at a horizontal "half pipe".
*If* we would have a omni speaker with a falling or rising FR we would see no colour changes along the vertical direction but colour changes along the horizontal lines – giving the impression of looking at a vertical "quater pipe".
So far so good.
Now what to expect form a real world horn?
As said earlier there are three distinct areas that differ quite remarkable in what they do. To understand that we have to recall that any horn is a "no horn" below a certain frequency – meaning it becomes sort of omni source the lower the frequencies get.
1.) the first area is the one where the directivity transition happens from omni to the "typical" beaming angle of the horn contour – you could say the horn hasn't (fully) got control over directivity in this department
2.) the second area is the one where the horn performs the horn task – controlling directivity and hence increasing SPL by concentrating acoustic energy to a certain room angle.
3.) the third area is the one where the horn lost control over directivity at its top end due to several reasons – mainly throat dimension and some other stuff I haven't got clear about yet
After this long wind up we easily can decode which of the two plots shown above are of more desire and which one can be expected to perform "better" – no?
Its the difference of "Swiss cheese defects" in the sound field - frequency by frequency overlaid one by the other - that makes all the difference.
The above plots are a compressed form to visualise exactly that – but don't confuse with "true" sound field plots that usually show behaviour at a single frequency only.
Michael
The data posted by John Sheerin and yourself illustrate several points I have previously made.
For instance the complex solutions to the Laplace equation in effect give you a set of orthogonal coordinates for a potential field that are dependent upon the duct boundary shape.
The outside of the horn can also be looked at as another potential field.
The utility of this is that there is a mapping that exists between two potential fields that preserves angle, known as a conformal mapping.
If we for instance take a conical horn with a perfect pulsating point source at its frustum then we have a perfect spherical wave expanding down the horn, and the field inside can be looked at as a perfect radially symmetrical potential field. The trouble is that we have to cut it at some point and let out the sound.
If we have an abrupt termination at an infinite baffle for instance the mapping from the inside of our horn is no longer a simple continuation of the field inside it but a diffraction field is superimposed upon it, the nature of which is determined at one end by the circumference, and the other by the diameter of the horn.
What we have to do to get an approach to the theoretical mapping between a potential field in and outside of our horn is to minimise the diffraction field superimposed upon it.
A flared section at the horn mouth in effect makes the aperture “fuzzy”, this is a technique that is used for instances in lasers to enable the formation of a Gausian beam.
Rcw.
For instance the complex solutions to the Laplace equation in effect give you a set of orthogonal coordinates for a potential field that are dependent upon the duct boundary shape.
The outside of the horn can also be looked at as another potential field.
The utility of this is that there is a mapping that exists between two potential fields that preserves angle, known as a conformal mapping.
If we for instance take a conical horn with a perfect pulsating point source at its frustum then we have a perfect spherical wave expanding down the horn, and the field inside can be looked at as a perfect radially symmetrical potential field. The trouble is that we have to cut it at some point and let out the sound.
If we have an abrupt termination at an infinite baffle for instance the mapping from the inside of our horn is no longer a simple continuation of the field inside it but a diffraction field is superimposed upon it, the nature of which is determined at one end by the circumference, and the other by the diameter of the horn.
What we have to do to get an approach to the theoretical mapping between a potential field in and outside of our horn is to minimise the diffraction field superimposed upon it.
A flared section at the horn mouth in effect makes the aperture “fuzzy”, this is a technique that is used for instances in lasers to enable the formation of a Gausian beam.
Rcw.
Good work, John and Michael! It's really good to see the quality of work you've put into this. Very much appreciated - and going into the lion's den of AA to make your first and second post took a bit of courage right there.
Fewer gurus, more data!!! (And yes, my avatar is strictly tongue-in-cheek, although the original pix was taken in India.)
Fewer gurus, more data!!! (And yes, my avatar is strictly tongue-in-cheek, although the original pix was taken in India.)
rcw said:
It's more than diffraction at the mouth with regard to reflections and what they *superimpose* on the output.
It's also diffraction as it relates to transition from a high pressure to a low pressure zone. This, (and not "combing"), is largely what is responsible for "ripple" - that goes so far as to modulate the entire output.
You can see this in CSD plots where strictly interference effects of combing would disturb the linear decay in a more pronounced manner than what "ripple" does. (..augerpro has some CSD plots that highlight this.)
Lynn Olson said:
Thanks!
panomaniac said:
Haven't measured / calculated but its been pretty much - around 10deg included but see it as a *very* rough estimation please – as to be honest – the "moon racer" happened by accident.
I tried to cut down the several thousand points of the contour to a reasonable quantity before importing into AxiDriver and lost the very beginning of the contour.
The resulting plot immediately told me to go back and have a closer look at the throat tangent angle.
If time (and faster equipment) allows, I'd like to come back to the topic of flare mis-match in a more structured way.
If you look at the light yellow colours you see that the overall shape is preserved between the two simus to some degree – its "just" ragged throughout versus pretty smooth but stunning enough - directivity over a wide frequency range still is "comparable" (well, sort of..).
ScottG said:
Uff
What I put forward Micheal was not a complicated translation into anything, but looking at a generalisation of the mathematics underlying such simulations.
The trouble I have with simulations is that when you try to find the limits and optimum values of things, or if they indeed exist, you quickly find yourself in the position of not being able to see the wood for the trees.
Genralisations such as this clear away most of the trees and we can then get a clear picture of the wood.
The envelope of a Gausian beam for instance is the wall contour of an o.s. waveguide, and the beam formed from a plane wave at the throat a very good approximation of one.
But in order for it to resemble one when let out into the room it needs a flared mouth section otherwise the diffraction field spoils things.
The near field wave guide I have described gives a very close approximation to a Gausian beam for a dome radiator, and has a single continuous curve, (I find that this is more esthetically satisfying than the former case).
You can show both of these things with simulation, but you have to start somewhere, and the formulation I described allows you to predict what you find before hand, with ideal plane and spherical waves etc. it is true, but that's where simulation comes in, and introduces vulgar number crunchings that allow you to simulate real transducers putting out real world wavefronts, via realisable wall contours.
This allows for the crossing of t's and the dotting of i's but the analytic generalisations determine the story, and many simulations I have seen produce very well edited nonsense.
rcw
The trouble I have with simulations is that when you try to find the limits and optimum values of things, or if they indeed exist, you quickly find yourself in the position of not being able to see the wood for the trees.
Genralisations such as this clear away most of the trees and we can then get a clear picture of the wood.
The envelope of a Gausian beam for instance is the wall contour of an o.s. waveguide, and the beam formed from a plane wave at the throat a very good approximation of one.
But in order for it to resemble one when let out into the room it needs a flared mouth section otherwise the diffraction field spoils things.
The near field wave guide I have described gives a very close approximation to a Gausian beam for a dome radiator, and has a single continuous curve, (I find that this is more esthetically satisfying than the former case).
You can show both of these things with simulation, but you have to start somewhere, and the formulation I described allows you to predict what you find before hand, with ideal plane and spherical waves etc. it is true, but that's where simulation comes in, and introduces vulgar number crunchings that allow you to simulate real transducers putting out real world wavefronts, via realisable wall contours.
This allows for the crossing of t's and the dotting of i's but the analytic generalisations determine the story, and many simulations I have seen produce very well edited nonsense.
rcw
andy19191 said:
Oh hell no!
I didn't purchase it. I am however contemplating the purchase of Solidworks premium (though for other reasons).
I don't know what the pricing structure is like - if it's like ProE, then it's just plain nutty. But I rather think it's somewhat more similar to Solidworks for price. i.e. you have the initial high expense depending on what sort of software package you want - THEN you have a much lower annual support/update fees *if desired*. (..could be wrong though.)