Mathcad versus Mathematica ... an old story !
When first in IBM, in the early 1981, I was teached how it was difficult to have a menu-based, user friendly, counterpart of a command-based environment.
I lived with this dicothomy during the years, with Windows and now with Audio and Mathematics.
Sure, the good news is that with Mathematica you have much more control than with Mathcad, the bad news is that you MUST have much more control.
There are other things that are worrying me: the role of the deferred evaluation, the way how Mathematica evaluates expressions, numerically versus symbolically, the rough way of handling units of measure (Mathcad is far superior in that), and so on ...
So ... I was unable to repeat the calculations I have done with Mathcad on the fiber behavour. Mathematica was so slow ! so slow that it was impossible to repeat the optimization I have done with the T/S parameters of the loudspeakr used by MJK. It is certainly my fault, that is of my inability of have a full control of Mathematica.
I shall show nextly how to do the Hilbert transform leading from the magnitude to the phase of a loudspeaker, using the Gauss-Tchebychev integration. It takes a few seconds ! (with Mathcad). These are the same calculations made by the "mytical" Paul Verdone in his spreadsheet (or, better, in his hundreds of VBA lines of code, impossible to decypher).
For the moment Mathcad is "good enough" for me.
What difficulties you had with it ?
When first in IBM, in the early 1981, I was teached how it was difficult to have a menu-based, user friendly, counterpart of a command-based environment.
I lived with this dicothomy during the years, with Windows and now with Audio and Mathematics.
Sure, the good news is that with Mathematica you have much more control than with Mathcad, the bad news is that you MUST have much more control.
There are other things that are worrying me: the role of the deferred evaluation, the way how Mathematica evaluates expressions, numerically versus symbolically, the rough way of handling units of measure (Mathcad is far superior in that), and so on ...
So ... I was unable to repeat the calculations I have done with Mathcad on the fiber behavour. Mathematica was so slow ! so slow that it was impossible to repeat the optimization I have done with the T/S parameters of the loudspeakr used by MJK. It is certainly my fault, that is of my inability of have a full control of Mathematica.
I shall show nextly how to do the Hilbert transform leading from the magnitude to the phase of a loudspeaker, using the Gauss-Tchebychev integration. It takes a few seconds ! (with Mathcad). These are the same calculations made by the "mytical" Paul Verdone in his spreadsheet (or, better, in his hundreds of VBA lines of code, impossible to decypher).
For the moment Mathcad is "good enough" for me.
What difficulties you had with it ?
Nice work Teodoro.
Paul and I worked on the MO extraction. His Excel based code used a discrete, FFT approach to MP reconstruction. The problem is that the FFT approach forces the phase to zero at the frequency extremes. Paul worked around that by some convoluted method that segments the frequency response and patch the results for each segment together. I tried to convince him to use the basic integral approach which I wrote a routine for and was very fast. I still do everything in FORTRAN and use FORTRAN routines called from EXCEL. I use Excel for a user interface and plotting. But the FORTRAN codes are much, much faster than using MathCAD.
Paul and I worked on the MO extraction. His Excel based code used a discrete, FFT approach to MP reconstruction. The problem is that the FFT approach forces the phase to zero at the frequency extremes. Paul worked around that by some convoluted method that segments the frequency response and patch the results for each segment together. I tried to convince him to use the basic integral approach which I wrote a routine for and was very fast. I still do everything in FORTRAN and use FORTRAN routines called from EXCEL. I use Excel for a user interface and plotting. But the FORTRAN codes are much, much faster than using MathCAD.
BIG chuckle here!! I too still do numerical analysis in FORTRAN!! There is nothing like it for speed. I use VB as a front end and and plotting since it is far more flexible than EXCEL. I am doing custom analysis software here in China for people who have never even heard of FORTRAN. I only laugh. I use MathCAD to develop the algorithm and then use FORTRAN when I get seriuos. I have MathCAD programs that take hours and FORTRAN does them in minutes.
I like MathCAD, always have, but when they were bought recently the customer service went all to He11. I really have not use Mathmatica enough to make a choice, and what you say could be quite true.
I like MathCAD, always have, but when they were bought recently the customer service went all to He11. I really have not use Mathmatica enough to make a choice, and what you say could be quite true.
More theory on polyester fiber in closed boxes
Has anybody visited here:
http://auralization.blogspot.com/?zx=5a5a0210d53820a4
It's a blog spot by Ken Kantor. However, the technical paper on PET fiber posted there is by John O Hanlon.
Has anybody visited here:
http://auralization.blogspot.com/?zx=5a5a0210d53820a4
It's a blog spot by Ken Kantor. However, the technical paper on PET fiber posted there is by John O Hanlon.
Thank you, I shall try to work on it.
I feel however that the measurements presented by JO tell only part of the thruth.The ideal measurements can be done only by an impedance tube, a two microphone technique and so on ...
The methods (mainly the measurement of the electrical impedance of a loudspeaker in a TL) used by MJK (on polyester fiber) and by R.A. Robinson (a student of Marshall Leach, on fiberglass) are just "good enough".
Some improvement, I guess, could be obtained by measuring the loudspeaker impedance not only with the "open" TL, bu also with the "closed" TL.
If the measurements are precise enough the could give both the (complex) speed of th sound and the (complex) density of the air.
I know, I should do the measurements ...
I have the loudspeaker, the tube ... I dont have yet the appropriate sound card to be used with Speaker Workshop.
Given my pace, it will take years !
I feel however that the measurements presented by JO tell only part of the thruth.The ideal measurements can be done only by an impedance tube, a two microphone technique and so on ...
The methods (mainly the measurement of the electrical impedance of a loudspeaker in a TL) used by MJK (on polyester fiber) and by R.A. Robinson (a student of Marshall Leach, on fiberglass) are just "good enough".
Some improvement, I guess, could be obtained by measuring the loudspeaker impedance not only with the "open" TL, bu also with the "closed" TL.
If the measurements are precise enough the could give both the (complex) speed of th sound and the (complex) density of the air.
I know, I should do the measurements ...
I have the loudspeaker, the tube ... I dont have yet the appropriate sound card to be used with Speaker Workshop.
Given my pace, it will take years !
I'm not sure who you were responding to above. However, read the O'Hanlon paper I provided a link to in an earlier post. It gives both theoretical and emperical evidence that FG performs a bit better than PET.
This paper looks a little bit suspicious.
It is out of the "mainstream" (that is it is mentioned by nobody working on the field; it not mentioned in the books of Cox-D'antonio and Bies-Hansen nor elsewere, as far as I know).
Same for Hersh and Walker, the authors of the flow resistivity model.
John O'Hanlon works since a long time as Vacuum Technology expert.
In any case I should ask to him for some clarifications.
I shall try to reproduce his calculations with the models I manage.
I don't want to repeat the discussion held by Villastrangiato about the Marek Natkaniec paper. When I asked for some clarification to Marek, he confessed that he wrote that paper when he was a student and since them he didn't work anymore on that topic. When requested to give some deeper understanding on that paper he gave up.
It is out of the "mainstream" (that is it is mentioned by nobody working on the field; it not mentioned in the books of Cox-D'antonio and Bies-Hansen nor elsewere, as far as I know).
Same for Hersh and Walker, the authors of the flow resistivity model.
John O'Hanlon works since a long time as Vacuum Technology expert.
In any case I should ask to him for some clarifications.
I shall try to reproduce his calculations with the models I manage.
I don't want to repeat the discussion held by Villastrangiato about the Marek Natkaniec paper. When I asked for some clarification to Marek, he confessed that he wrote that paper when he was a student and since them he didn't work anymore on that topic. When requested to give some deeper understanding on that paper he gave up.
I guess the emperical data (e.g. impedance measurements) aren't convincing enough to show FG's improved performance as a stuffing medium.
In any case, few, if any, mfgr's use FG any more simply because of the safety issues involved. The difference is slight enough for them to choose the safer fiber.
Looking at that "famous" paper I went on eq. (14), that should express the impedance of a closed (open ?) tube.
It was not correct, at least in my opinion. I rechecked my calculations, but it was still incorrect. Then I saw also that also Gary Scavone wrote:
Zal=-i Z0 cot(k L) (or Zal=-j Z0 cot(k L), if you are an engineer ...) for a closed pipe and Zal=i Z0 tan(k L) for an open piper (negletting at all the radiation impedance at the open end) [page 13 of his Ph.D. thesis]. Z0=rho c/S (the section of the duct).
Gary Scavone (Gary Scavone @ McGill) is now Associate Professor at McGill University, so I guess he is much clever than me.
So I read, and I re-read the O'Hanlon paper, in order to understand his reasonings.
Please help !
It was not correct, at least in my opinion. I rechecked my calculations, but it was still incorrect. Then I saw also that also Gary Scavone wrote:
Zal=-i Z0 cot(k L) (or Zal=-j Z0 cot(k L), if you are an engineer ...) for a closed pipe and Zal=i Z0 tan(k L) for an open piper (negletting at all the radiation impedance at the open end) [page 13 of his Ph.D. thesis]. Z0=rho c/S (the section of the duct).
Gary Scavone (Gary Scavone @ McGill) is now Associate Professor at McGill University, so I guess he is much clever than me.
So I read, and I re-read the O'Hanlon paper, in order to understand his reasonings.
Please help !
There is not enough info from your post to answer without doing a lot of digging. What is equation 14? Is this the equation for the impedance at one end of a pipe of length L, with the other end rigid? For th open pipe, is the load assumed to be zero?
If you use a T-matrix, it is easy to derive the correct form for both cases. In one case the velocity is zero at the far and and in the other the pressure is zero. Then solve for the impedance at the near end.
If you use a T-matrix, it is easy to derive the correct form for both cases. In one case the velocity is zero at the far and and in the other the pressure is zero. Then solve for the impedance at the near end.
Eq.(14) looks like:
z(0,t)=(p0 Gamma P / w) tanh ( Gamma L)
w should be omega = 2 pi f (the frequency), Gamma is somehow the effective "propagation constant" (that would be w / c without filling, with some +i or -i: I should check the definitions).
So, ok, eq. (14) resembles to the equation for the impedance of an OPEN pipe.
But ... the AR-3a and AR-11 where CLOSED boxes, or not ?
z(0,t)=(p0 Gamma P / w) tanh ( Gamma L)
w should be omega = 2 pi f (the frequency), Gamma is somehow the effective "propagation constant" (that would be w / c without filling, with some +i or -i: I should check the definitions).
So, ok, eq. (14) resembles to the equation for the impedance of an OPEN pipe.
But ... the AR-3a and AR-11 where CLOSED boxes, or not ?
Something wrong here - "z(0,t)" ?? What is "t" ?, can't be time because impedance as a function of time would be highly nonlinear. Gamma woud be the complex wavenumber - I was going to ask why your equations used a real wavenumber. The usual way to represent continuous absorption is with a complex wavenumber, ie. assume the wave propagates as e^ (i* Gamma * x) with Gamma complex (it has both real and imaginary parts) and the amplitude will decrease with x. This is how I have always done the problem.
No, gedlee, no, please !
"My" equation is Zal=i Z0 tan(k L).
Eq. z(0,t)=(p0 Gamma P / w) tanh ( Gamma L) is the equation (14) of O'Hanlon.
"My" equations would be even more complex. It would include the output radiation term (Lord Raileigh if "flanged" or even Levine-Schwinger if "unflanged"), Z0 and k had become the "equivalent fluid" representations for the characteristic impedance and wave number.
So, it seems that you had never opened that paper ! If you did, you would ask those questions to O'Hanlon, not to me.
Again: on what papers is based your "perfectly sufficient" understanding on fiber behaviour ?
Being more serious ... it seems that there is something wrong on the assumptions (I'm still investigating on them) that the properties of a model depend only on flow resistivity, and that flow resistivity depends only on fiber density (and diameter).
As an example let me show the Absorption Coefficient for fibers of different diameters and density:
E.g., to get the same absorption of 5 kg/m3, 50 mm, of a fiber having diameter 5 micrometers (fiberglass diameter ranges from 5 to 15 micrometers), we need 75 kg/m3 of a fiber having diameter 33 micrometers (typical polyester fiber).
It seems to me unrealistic that at such densities the models for the polyester fiber stay valid.
These are the things for which I have insufficient understanding. And you ?
"My" equation is Zal=i Z0 tan(k L).
Eq. z(0,t)=(p0 Gamma P / w) tanh ( Gamma L) is the equation (14) of O'Hanlon.
"My" equations would be even more complex. It would include the output radiation term (Lord Raileigh if "flanged" or even Levine-Schwinger if "unflanged"), Z0 and k had become the "equivalent fluid" representations for the characteristic impedance and wave number.
So, it seems that you had never opened that paper ! If you did, you would ask those questions to O'Hanlon, not to me.
Again: on what papers is based your "perfectly sufficient" understanding on fiber behaviour ?
Being more serious ... it seems that there is something wrong on the assumptions (I'm still investigating on them) that the properties of a model depend only on flow resistivity, and that flow resistivity depends only on fiber density (and diameter).
As an example let me show the Absorption Coefficient for fibers of different diameters and density:
An externally hosted image should be here but it was not working when we last tested it.
E.g., to get the same absorption of 5 kg/m3, 50 mm, of a fiber having diameter 5 micrometers (fiberglass diameter ranges from 5 to 15 micrometers), we need 75 kg/m3 of a fiber having diameter 33 micrometers (typical polyester fiber).
It seems to me unrealistic that at such densities the models for the polyester fiber stay valid.
These are the things for which I have insufficient understanding. And you ?
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