How to calculate and plot a function with continous(input data) and constant variables

Question

First step (done):

I start with my concrete problem: (sry for posting the full code, but might be better understanding)

Variables:

ρ0 := 1.2041;
P := 0.95;
G := 100000;
f := 6000;
ω := 2*Pi*f;
η := 1.85*10^-5;
j := 1.4;
P := 0.71;
B := Sqrt[P];
P0 := 101325;
(*k & z for f=6000*)
k = 170.09 - 82.22 I;
z = 676.6 - 330.61 I;

some simple equations:

α = (G*P)/(ρ0*ω)

k2 = Sqrt[z^2/(k/ω)^2]
ρ = z^2/k2

And the function with the searched variables "r" and "e":

Solve[ρ == ρ0*α*(1 + (P*G)/(
      I (ω*ρ0*α))*(1 + 
        I (4*ω*ρ0*η*α^2)/(G^2*P^2*r^2))^(
      1/2)), r]

Solve[k2 == P0/(
  j - (j - 1) (1 + (8*η)/(
       I (ω*B^2*e^2*ρ0))*(1 + 
         I (ω*B^2*ρ0*e^2)/(16*η))^(1/2))^-1), e]

My problem right now is that the variable f (=frequency) is continous (somewhere from 350 to 6400 in step 0.5).To every frequency there is a corresponding k and z.

I have my values for f , k and z in two .txt files. See at the end, there is a short ectract.

So, how to import these data correctly from the .txt-file (e.g. with space character between real and imaginary number) and solve, respectively, plot the searched variables "r" and "e" as a function of "f" with corresponding "z" and "k"?

I hope for concrete answers to my problem.

Thanks a lot!

f in Hz Re(k) in 1/m    IM(k) in 1/m

300 18,1021587151   -20,268568883
301 17,8270460036   -19,9416539488
302 17,574903357    -19,7650284049
303 18,8974277344   -19,344621652
304 18,799546006    -18,4230245471
305 19,3050841571   -18,0620751669
306 20,0889951843   -17,3210376494
307 21,1941412976   -17,0011098871

f in Hz Re(Z) in Ns/m^3 IM(Z) in Ns/m^3

300 1889,32930532   -1282,64805963
301 1924,55593429   -1283,96093068
302 1927,73749935   -1313,43266941
303 1846,3736042    -1331,9786319
304 1901,82478069   -1305,0076572
305 1903,96509609   -1310,07794373
306 1889,26900477   -1348,41152746
307 1853,51057624   -1344,98426415

Second step:

I want to inverse this method. So again my variables,

\[Rho]0 := 1.199;
\[Phi] := 0.97;  
\[Sigma] := 47742.675; 
\[Omega] := 2*Pi*f;
f = [(1000, 6300)];
\[Eta] := 1.81*10^-5;
\[Kappa] := 1.4;   
Pr := 0.72; 
B := Sqrt[Pr]; 
P0 := 98900;  
\[Lambda] = 1.296*10^-5;    
\[Xi] = 6.963*10^-5; 
\[Alpha] = 1;    
ko = \[Eta]/\[Sigma]; 
d = 14.1*10^-3;  
c0 = 345.53841;

But now, I want to solve following equations in dependency of frequency (f=1000-6300; how to define the steps?) AND for each frequency for different angle values [Epsilon] = [(0°, 90°)](define the single steps?). The aim is the average value of tau for each frequency of different angles.

Try of solve, export and plot the result.

result = Map[(f;
    z = Sqrt[k2*\[Rho]]; k = \[Omega]*Sqrt[\[Rho]/k2]; 
    Zs = z*coth[-I*k*d]; 
    R = (Zs/(\[Rho]0*c0)*cos (\[Epsilon]) - 1)/(Zs/(\[Rho]0*c0)*cos (\[Epsilon]) + 1); 
    \[Tau] = 1 - Abs[R]^2;
    {f, Solve[\[Rho] == \[Rho]0*\[Alpha]*(1 + (\[Phi]*\[Sigma])/(I (\
\[Omega]*\[Rho]0*\[Alpha]))*(1 + 
              I (4*\[Omega]*\[Rho]0*\[Eta]*\[Alpha]^2)/(\[Sigma]^2*\
\[Phi]^2*\[Lambda]^2))^(1/2)), \[Rho]], 
     Solve[k2 == 
       P0/(\[Kappa] - (\[Kappa] - 
             1) (1 + (8*\[Eta])/(I (\[Omega]*
                    B^2*\[Xi]^2*\[Rho]0))*(1 + 
                  I (\[Omega]*B^2*\[Rho]0*\[Xi]^2)/(16*\[Eta]))^(1/
                  2))^-1), k2], z, k, Zs, R, alpha})];

Export["result.txt", result];
Print[ListPlot[Map[{#[[8]]} &, result], 
   PlotLabel -> "\[Tau] versus f"]];

If there are again more solutions for the absolut value, there is only necessity of one of them.

Thanks a lot again!

Answer 1

I don't know whether in your location a comma is the default separator for decimal numbers. Here the period is the default separator. To make this code slightly simpler I have manually changed all the , to . in your two text files.

Do your variable initalizations and then

rawk = Import["kdata.txt", "Data"];
fmtk = Map[{#[[1]], #[[2]] + I*#[[3]]} &, rawk];
rawz = Import["zdata.txt", "Data"];
fmtz = Map[{#[[1]], #[[2]] + I*#[[3]]} &, rawz];
fmtkz = MapThread[Join, {fmtk, fmtz}];

reads the two data files, constructs each Complex from the two parts and finally joins the k and z for each row of your data file.

Then

result = Map[
   (f = #[[1]]; k = #[[2]]; z = #[[4]];
    α = (G*P)/(ρ0*ω); k2 = Sqrt[z^2/(k/ω)^2]; ρ = z^2/k2;
    {f, α, 
     Abs[r /. Solve[ρ == ρ0*α*(1 + (P*G)/(I (ω*ρ0*α))*(1 + 
       I (4*ω*ρ0*η*α^2)/(G^2*P^2*r^2))^(1/2)), r][[2]]], 
     Abs[e /. Solve[k2 == P0/(j - (j - 1) (1 + (8*η)/(I (ω*B^2*
       e^2*ρ0))*(1 + I (ω*B^2*ρ0*e^2)/(16*η))^(1/2))^-1), e][[2]]]
    })&, fmtkz];
Export["result.txt", result];
Print[ListPlot[{Map[{#[[1]], #[[3]]} &, result], 
   Map[{#[[1]], #[[4]]} &, result]}, PlotLabel->"Abs[r] and Abs[e] versus f"]];
Print[ListPlot[Map[{#[[1]], #[[2]]} &, result], PlotLabel -> "α versus f"]];

will take each row of your combined k and z, do the two Solve and give you the result.

EDIT: Revised to discard multiple roots, format and Export the results and ListPlot the results