Dual axis function

[ELSID]

I am trying to chart a function with respect to sound on one axis and surface area on the other. When I plug in values for the variables, I get a value. However, i can not get the chart to correlate. Scaling issue?

[TomGutman]

I don't undestand the problem. But note that dual y axes is not a feature of MC11, and you lose secondary axes if you save into MC11 format.
__________________
� � � � Tom Gutman

[ELSID]

Tom,
File re-posted as version 14.

[ptc-1368288]

On 11/19/2009 7:44:50 PM, ElSid wrote:
>I am trying to chart a
>function with respect to sound
>on one axis and surface area
>on the other. When I plug in
>values for the variables, I
>get a value. However, i can
>not get the chart to
>correlate. Scaling issue?
____________________________

Nothing makes sense.

The scalar function is the trig, so you must plot vs the argument of the function, i.e: atan(u). What is /dB ? that kind of invention is not needed. The other point is about the export, but at least get an X, Y plot first.

>I am trying to chart a
>function with respect to sound
>on one axis

==> OK, that is in one direction

>and surface area on the other.

==> That's the other direction,

No problem but you must then express the area in that direction.
Something like f(sound, area):= sound,area
Look the qs for similar type of parametric plot.
Have a look at the user manual for G(u,v):= X(u,v), Y(u,v), Z(u,v) where X,Y,Z are in vector form.

A quickplot is not a chart ! only quickplot.
For a chart, you need a data table export.

jmG

[ELSID]

The dB and /dB is a user definition for sound (credit to Tom). I've been working on some calculations and this item came up. I posted the equation/function and I want to post left y-axis change in dB (which the function calculates), right y-axis (surface area) all with respect to distance. I have a similar published graph (different function). See attached

[AlvaroDíaz]

On 11/20/2009 3:05:36 AM, ElSid wrote:
>...See attached

In the attached you have a level-curve plots, I don't see a dual axis concept there.

Regards. Alvaro.

[RichardJ]

This graph does not have a right y-axis. What you have is not a problem that requires left and right axes. You have a function of two variables, area and distance. You can plot a family of curves, for different areas, on a graph with axes for distance and dB. Or you could plot a family of curves, for different distances, on a graph with axes for area and dB. Or you could create a 3D plot. If you want to create a family of curves, there are better ways to do it.

Richard

[ptc-1368288]

On 11/20/2009 3:05:36 AM, ElSid wrote:
>The dB and /dB is a user
>definition for sound (credit
>to Tom)...
_____________________________

YES for /dB, also |dB ... etc.

You don't handle Mathcad correctly on all these counts +++. You take formulas from foreign source, very few formulas from old literature are executable in Mathcad, they all need be interpreted and reconstructed. You must always get a plot from the very beginning and never use subscripts before you have something visible. Your formula with Lp is not correct, it simplifies by inspection and Mathcad confirms. The argument on the X axis is the scalar argument of the scalar function, in this case (u) ... the scalar function is atan(u) ... (x) is the parameter that will plot multiple times the same function but with the valued scaling as per (x).

Your main formula is either wrong or the plot from the picture is a draftsman construct in pieces, the global formula does not reproduce as a raw formula. It might be possible piecewise. What Richard is telling is what I'm illustrating in the attached. Yes, it is a bit difficult to agglomerate all collaborations because of the immediate interpretation from individuals and the time each can spend and how far from realistic is the work sheet from the poster. Often, the collab is nearly there but in your case with things that cover a book and badly concluded ... lot more difficult.

A good example of old literature and the interpretation is Viktor reply about pseudo-inverse for chemical reactions. Viktor did it from a more recent literature than the one I was reading and pedalling to interpret. You must put + effort trying to handle Mathcad as it is, a superb tool for Engineers. How many math formulas can you put directly from Wiki to Mathcad = NONE !. How many from papers to Mathcad = about NONE ! unless the paper is a Mathcad paper. Mathcd is essentially a "scalar math tool" therefore more different than Matlab, Scilab, ...etc.

jmG

[ELSID]

Thank you Richard and jmG. Richard got a graph similar to what I wanted, was about to ask question until I saw jmG response. will chew on what was said and repost.
BTW jmG, A.vs is a substitution for height * width. I locked in height.

UPDATE: Posted new sheet.
jmG I noticed you re-defined some of my dB functions. Please explain?

[ptc-1368288]

On 11/20/2009 12:59:56 PM, ElSid wrote:
...
>A.vs is a substitution for
>height * width.
___________________________

You had A subscripted vs, i.e: a variable name called 'x' or whatever . If Avs is in your mind A*vs, you must tell Mathcad to multiply A by vs.


jmG

[ptc-1368288]

On 11/20/2009 12:59:56 PM, ElSid wrote:
....
jmG I noticed you
>re-defined some of my dB
>functions. Please explain?
____________________________

You return my work sheet, not yours.

Explain what ?
You have the book, I don't see so far so through/true.
What do you want ? Plot the book graph you have posted ? no problem: construct the book plotting formula or if you can't, give the book formulas.

jmG

[AlvaroDíaz]

On 11/20/2009 12:59:56 PM, ElSid wrote:
>Thank you Richard and jmG. Richard got a graph similar to what I wanted, ...

But probably you need to extract the data from the picture and not have the analitic expression. If it is the case, here there a free tool to do this:

Spline2xV6: Karolewski and Richard's wrappers:
http://collab.mathsoft.com/~Mathcad2000/read?110936,21

The discussion actually cames from:

Gas turbine perfomance plots:
http://collab.mathsoft.com/~Mathcad2000/read?110906,21

For the first approach do this: download Karolewski softare and extract the data from the plots by hand, paste the tables into mathcad and interpolate for each iso-level curve.

Further, you can try the more advanced (and semi-automated) methods described in the post (there are 4 or 5 techniques).

Regards. Alvaro.

[ELSID]

Alvaro, this is a bonus! Still working with the other equation. The equation came from a document several photo copies old (photo of a photo of a photo...). I just magnified and found a sqrt in the denominator. Will re-post corrected version shortly.

[ptc-1368288]

On 11/20/2009 3:58:51 PM, ElSid wrote:
...
>Still working with the other
>equation. The equation came
>from a document several photo
>copies old (photo of a photo
>of a photo...). I just
>magnified and found a sqrt in
>the denominator. Will re-post
>corrected version shortly.
_______________________________

Waiting for the working formula that plots. That plots from photo/photo/photo/magnified. Is that document valid/certified/part of a regulation ? An outdated regulation ? Why not used the most up date regulation. Is the project to be redone ? redone for what reason ? Any pocket calculator should solve, Excel too. If there is a function, why digitizing ? Digitizing is not so simple and with that kind of picture it will need some caution. Finally, the Mathsoft digitizer did a better job in that link than the other in reference. Did you miss Valery digitizer [July 2009].

jmG

[AlvaroDíaz]

On 11/20/2009 7:27:57 PM, jmG wrote:
>Did you miss Valery digitizer [July 2009].

Yes, I do because I don't nver see this (very recent) digitizer that you say ... traying to searching.

Regards. Alvaro.

[TomGutman]

As Richard points out, you don't have dual axes, rather you have a family of curves. The picture shows the traces labeled with the parameter value they represent, there is no way to do that in Mathcad. You can do a family of curves, in various ways. But note the wide spread of the area variable in te picture -- attempting a family with closely spaced areas results in curves so closely spaced as to be unreadable.

It's not clear exactly what you want to show, generally I prefer 3D graphs (surfaces) to show functions of two variables.
__________________
� � � � Tom Gutman

[ELSID]

Chart going the wrong way. At wits end. Asking for help in highlighted region

[StuartBruff]

On 11/20/2009 5:36:16 PM, ElSid wrote:
>Chart going the wrong way. At
>wits end. Asking for help in
>highlighted region

Sorry, only got time for a very quick look - some
3D stuff attached.

Stuart

[ELSID]

Stuart,

I understand that dist 0 caused a singularity, was actually a jmG suggestion to eliminate what I called the "loop back" Sloped line going back to next curve. Change in dB should increase with distance. The further you are, the softer it gets (change from initial source is increasing. Shouls h and w be combined into a single argument? I did that earlier but surface area is not 1 to one ... though it made sense. Hmm will think about.

Think I found fundamental HUGE error. Equation should be Lp MINUS ... Not divided.

[TomGutman]

What "way"? And what "way" is right?
__________________
� � � � Tom Gutman

[ptc-1368288]

On 11/20/2009 5:36:16 PM, ElSid wrote:
>Chart going the wrong way...
_____________________________

As it looks: YES

Three variables will "QuickPlot" as well as export. The matter is the right formula that many collabs are waiting for. The green line is about where the draftsman decided to split or invent the leftmost portion or simply define a piecewise global function. How do you estimate /dB(,) below 1 ?

jmG

[ELSID]

jmG,
Chart is from source that that can no longer be traced. Equation is from an article from Acoustic Society of America (~2004) and I do not have the full article. I was told they chart and formula) correlate well and was trying to model it.

The division in the formula is correct per the procedures previously discussed with Tom. The only modification from the articles formula is that I am eliminating the initial sound intensity to get a change. As I get further from the source, the change should get bigger (see the chart). I aexpected a graph similar to this, just mirrored about change ~14 dB.

[ELSID]

After a little # crunching (sleep & food), I figured out that the equation was not a change in dB but a % of the original intensity (I hate the fact that I do not have the full articles)! 3d charts by Stuart, did not check. Looking for sanity check of Mathcad procedure correctness maybe even optimization hints and tricks.

[ptc-1368288]

On 11/21/2009 3:45:29 AM, ElSid wrote:
...
>Looking for sanity check of
>Mathcad procedure correctness
>maybe even optimization hints
>and tricks.
______________________________

No sanity would apply if you don't have a reference.
On my side, the project can sleep in the recycle bin.



You need the formulation in the
X direction, in the Y direction and in the Z direction... to plug in the formula in example or in the matrix form.

jmG

[TomGutman]

It's a fraction of the original intensity (% implies an additional factor of 100). Such a fraction can be expressed simply as a fraction, or it can be expressed in dB (as you did).

As to matching your posted chart -- maybe. The comments on that chart seem to indicate that the plotted values are not the total change in intensity, but rather an adjustment to a simple inverse square law.
__________________
� � � � Tom Gutman

[ELSID]

Correct, It is an adjustment to the sound power. It should NOT match the chart as they come from different sources. I am using a point on the chart to find a correlation between the two and dind alpha (absorption parameter). I wish I had the whole article. The only available information is a photocopy of a cut out that has seen better days.

[TomGutman]

How can you find α in an equation that give the overall sound reduction by matching that to a sound intendity adjustment? To be meaningful, you have to equate like with like. If you don't expect the curves to be the same, why do you expect that particular value to be the same?
__________________
� � � � Tom Gutman

[ELSID]

Two differing trains of thought.

jmG, I can probably buy the issue of the ASA journal if needed. Problem is that the formula has never been used in my particular application. Curve has lost traceability. Like you say ... ZAP, but used by other "experts" in the field. I tend not to follow by attrition so I want to correlate between the two. I have tried to answer all questions and suggestions as they arise. Will read jmG last comment and see if I missed something.

Tom, for the formula to work, an empirical solution for alpha is needed. By modifying the equation which solves for the overall sound equation to give an adjustment, I am equating like with like. Example 84 dB equates to 81 dB using equation. By subtracting initial with final, I can compare deltas ... like with like. Logic is there for me, suggestions are welcome.

Val, I do not understand what you are trying to show on your post.

[TomGutman]

But did you make the adjustment to the sound intensity equation? That equation looks like it is doing an overall intensity calculation, not an adjustment to an inverse square law.

Further -- if α is to be found empirically (presumably dependent on the details of the environment) what is your justification for assuming that your setup is sufficiently similar to that used for those particular curves to be able to determine your value of α from the published curves? You've described it as an absorbtion coefficient, which I would expect to be dependent on the particular material used for the tunnel walls.
__________________
� � � � Tom Gutman

[ptc-1368288]

On 11/22/2009 7:03:19 PM, ElSid wrote:
...>Curve has lost traceability.
>Like you say ... ZAP, but used by other
>"experts" in the field.
...
Val,
>I do not understand what you
>are trying to show on your
>post.
_____________________________

>but used by other
>"experts" in the field.

==> formula is lost, graph is used by experts ...
==> then don't go the expert way, go the Engineer way. The attached is brute force, guessed less than � hour job. And a data table for export and republish the "lost world" c/w formula that can be used by any serious math or semi-math tool like Excel. The graph does not result from a single function as mentioned previously.



A last question:
So, you just have a graph and no data table.
What's the problem passing what you have as formula ? I bet some collab will interpret that plotting formula, you seem stuck trying to interpret a working formula.

jmG