Author: Roman Chijner, Heidelberg
Date: 2012

Input N_P

      x    y   z
fx: tx   x   y
fy: x    ty  y
fz: x    y   tz

z_{min}= :

z_{max}= :

Zoom

N_P(≤1000) =:

\scalebox{1.5}\text{Verteilung der Auslenkungen bei Interferenz zweier Kreiswellen} 

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$\scalebox{1.4} \text{\copyright Roman Chijner, Heidelberg 2013}$
$\scalebox{1.3} \text{     Gestaltungshilfe:}\scalebox{1.3}\text{ Werner Knobloch}$

x

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Methode:  Roots

Genauigkeit:

N_{V1}(≤1000) =:

N_{V2}(≤400) =:

x

Set Linienstärke 1-13:

→

►

◄

►

◄

►

◄

←X→

↑Y

Y↑

Z∙ 

a/b

Methode: \fgcolor{red}{R}oots\fgcolor{red}{B}y\fgcolor{red}{L}ocus

bewegtes Rechteck +

Auflösung:

0

+

Zoom +

Zoom -

Bildschirmausschnitt:
(blaue Punkte bewegen)

Größe setzen

Spur setzen

Spur

Punkteigenschaften:

refresh

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►

Intervall_{x,y}:[ -a_0,a_0]

refresh

Animation

►

II←

◄

δ =:

T =:

λ =:

Δφ =:

t_T=:

A_z(x,y,t)=A_0 exp(-\delta*r_{s_1}(x,y))*sin(\frac{2\pi }{\lambda}*r_{s1}(x,y)-wt)+A_0 exp(-\delta*r_{s_2}(x,y))*sin(\frac{2\pi }{\lambda}*r_{s2}(x,y)-wt+Δϕ)

Auslenkung-Animation

Knoten & Bäuche

$\text{     \fgcolor{cyan}{Knoten} und \fgcolor{ff9900}{Bäuche}      $

$$

II←

►

◄

t_A=:

Wellenparameter:

Zeitverlauf:

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I. Spurplot

II. Feste Linien

b) Regionsfärbung

a) Linienplot

N_{V1}(≤5000) =:

Feste Punkt-Linien

    Plottfarben:                                            


           
                                                                

    Ausschnitt           
    Hntergrund:  





             

nur \fgcolor{red}{R}oots\fgcolor{red}{B}y\fgcolor{red}{L}ocus

T = 10 (slider from 0 to 50, step 0.1)
t_T = 0 (slider from 0 to T, step 0.02)
t_A = 0.5 (slider from 0 to 1, step 0.02)
zz1: -2 + (4 * t_A)
Δφ = 0 (slider from 0 to 6.283185307179586, step 0.1)
λ = 18 (slider from 0 to 50, step 0.1)
δ = 0.02 (slider from 0 to 1, step 0.01)
S_2 = (30, 0)
S_1 = (-30, 0)
zz = 0 (slider from -2 to 2, step 0.01)
a_0 = 10 (slider from 5 to 40, step 5)
Ro = (-40, -40)
Rob: (200, y(Ro))
py = Ray(Ro, Rob)
Ro1 = Point(py)
Roa: (x(Ro), 200)
px = Ray(Ro, Roa)
Ro2 = Point(px)
Roo: (x(Ro1), y(Ro2))
Roo' = (40, 40)
Ro' = (-40, -40)
s = -1 (slider from -1 to 1, step 2)
ε = 0.5 (slider from 0 to 1, step 0.05)
N_P = 150
b = false
z_{max} = 40 (slider from -40 to 40, step 0.1)
N_1 = If(b, N_P, 4)
z_{min} = -40 (slider from -40 to 40, step 0.1)
f(x, y) = (ℯ^(((-δ) * sqrt((x - x(S_1))^(2) + (y - y(S_1))^(2)))) * sin(((2 * π / λ) * sqrt((x - x(S_1))^(2) + (y - y(S_1))^(2))) - ((2 * π / T) * t_T))) + (ℯ^(((-δ) * sqrt((x - x(S_2))^(2) + (y - y(S_2))^(2)))) * sin(((2 * π / λ) * sqrt((x - x(S_2))^(2) + (y - y(S_2))^(2))) - ((2 * π / T) * t_T) + Δφ)) - zz1
O = Intersect(yAxis, xAxis)
y_{min}: y(Ro')
y_{max}: y(Roo')
Δt = 0.02 (slider from -5 to 5, step 0.1)
inputBox3 = Textfield(z_{min})
inputBox5 = Textfield(z_{max})
SFactor = 1 (slider from 0.5 to 2, step 0.1)
x_{max}: x(Roo')
tlmax1: x_{max}
tlmax2: y_{max}
x_{min}: x(Ro')
tlmin1: x_{min}
tlmin2: y_{min}
trmax1: y_{max}
trmax2: x_{max}
trmin1: y_{min}
trmin2: x_{min}
inputBox7 = Textfield(N_P)
tt1 = Sequence(tlmin1 + ((tlmax1 - tlmin1) / N_1 * i), i, 0, N_1)
tt2 = Sequence(tlmin2 + ((tlmax2 - tlmin2) / N_1 * i), i, 0, N_1)
P2yyx = If(b, Join[Zip[Reverse[{Roots[f(x, b), trmin2, trmax2]}] + (0, b), b, tt2]], {(1000, 1000)})
poly1, a_1, b_1, c_1, d_1 = Polygon(Ro, Ro1, Roo, Ro2)
P1xxy = If(b, Join[Zip[Mirror[{Roots[f(a, x), trmin1, trmax1]}, y = x] + (a, 0), a, tt1]], {(1000, 1000)})
Px1: (x_{min}, 0)
Px2: (x_{max}, 0)
Py1: (0, y_{min})
Py2: (0, y_{max})
Pz1: (z_{min}, 0)
Pz2: (z_{max}, 0)
N_{V1} = 200 (slider from 0 to 10000, step 1)
m1 = 201 (slider from 1 to N_{V1} + 1, step 1)
dx: (x_{max} - x_{min}) / N_{V1}
dy: (y_{max} - y_{min}) / N_{V1}
dz: (z_{max} - z_{min}) / N_{V1}
xi: x_{min} + ((m1 - 1) * dx)
yi: y_{min} + ((m1 - 1) * dy)
zi: z_{min} + ((m1 - 1) * dz)
Ax = Point(Segment[Px2, Px1])
Ay = Point(Segment[Py2, Py1])
Az = Point(Segment[Pz2, Pz1])
fxx(x) = f(x, y(Ay))
fyy(x) = f(x(Ax), x)
B1xx = If((fxx(xi - ε / 2) * fxx(xi + ε / 2))  <  0, (xi, y(Ay)))
B1yy = If((fyy(yi - ε / 2) * fyy(yi + ε / 2))  <  0, (x(Ax), yi))
N_{V2} = 80 (slider from 0 to 500, step 10)
inputBox12 = Textfield(N_{V1})
inputBox13 = Textfield(N_{V2})
dx2: (x_{max} - x_{min}) / N_{V2}
dy2: (y_{max} - y_{min}) / N_{V2}
B = (0.07356189171039254, 0.054935288899808296)
dz2: (z_{max} - z_{min}) / N_{V2}
a = 4 (slider from 1 to 13, step 1)
ta: z_{min}
tb: z_{max}
e = false
Bxx3 = If(fxx(xi) > 0, (xi, y(Ay)))
Bxx4 = If(fxx(xi)  <  0, (xi, y(Ay)))
loc1xx = If(e, Locus[B1xx, Ay], Locus[Bxx3, Ay])
locxx2a = If(¬e, Locus[Bxx4, Ay])
loc1yy = If(e, Locus[B1yy, Ax])
Info1: " t_T = " + (LaTeX[t_T]) + " ,T = " + (LaTeX[T]) + " , S_1 = " + (LaTeX[S_1]) + " , S_2 = " + (LaTeX[S_2]) + " ,  A_0 = 1 , A_z = " + (LaTeX[zz1]) + " , λ = " + (LaTeX[λ]) + " , δ = " + (LaTeX[δ]) + " ,  Δϕ = " + (LaTeX[Δφ]) + " , ε = " + (LaTeX[ε]) + "  
                         Intervall_x= [" + (LaTeX[x_{min}]) + "," + (LaTeX[x_{max}]) + " ]  ;  Intervall_y= [ " + (LaTeX[y_{min}]) + ", " + (LaTeX[y_{max}]) + "]  ;  Intervall_z= [" + (LaTeX[z_{min}]) + " ," + (LaTeX[z_{max}]) + " ]"
o = true
q = 3 (slider from 1 to 4, step 1)
r = true
poly1a, j, k, e_1, f_1 = Polygon(((-a_0), (-a_0)), (a_0, (-a_0)), (a_0, a_0), ((-a_0), a_0))
v = true
w = false
Textfeld4 = Textfield(δ)
Textfeld3 = Textfield(T)
Textfeld5 = Textfield(λ)
inputBox4 = Textfield(Δφ)
Textfeld1_1 = Textfield(t_T)
c = false
L = Distance(S_1, S_2)
xxxl2max11 = KeepIf(abs(x) ≤ L / 2, Sequence[(i * λ / 2) - (Δφ * λ / ((4 * π))), i, -20, 20])
xxxl2min11 = KeepIf(abs(x) ≤ L / 2, Sequence[(i * λ / 4) - (Δφ * λ / ((4 * π))), i, -21, 21, 2])
βge = Angle(Line[S_1, S_2], xAxis)
h = true
inputBox1 = Textfield(t_A)
ttA: 1 - (5 * (t_A - 0.5))
Sα = Angle(Line[S_1, S_2], xAxis)
zmaxar = Sequence(Hy[S_1, S_2, Element[xxxl2max11, i]], i, 1, Length[xxxl2max11])
zminar = Sequence(Hy[S_1, S_2, Element[xxxl2min11, i]], i, 1, Length[xxxl2min11])
xminEllipse = KeepIf(abs(x) ≥ L / 2, Sequence[(i * λ / 2) - (Δφ * λ / ((4 * π))) + (λ / T * t_T), i, 0, 20])
zminE = Sequence(Ellipse[S_1, S_2, Element[xminEllipse, i]], i, 1, Length[xminEllipse])
Textfeld1 = Textfield(N_{V1})
Autor1: "" + (LaTeX[Autor]) + ""
Text9: "x_{min}= " + x_{min} + "    x_{max}= " + x_{max} + " "
text7: "y_{min}= " + y_{min} + "    y_{max}= " + y_{max} + "  "
text20: "Projektionsachse (PA): z      A_z = " + (LaTeX[zz1]) + ""
text18: "A_z∈[-2,2]   t_A∈[0,1]   A_z= -2+4· t_A= " + zz1 + "  "
Info2: "" + (LaTeX[Info1]) + ""
A = (50.813640623472764, 3.8234193572543305)
C = (50.67884106936012, -0.6249659284630459)
Fr_x = 0 (slider from 0 to 1, step 0.1)
Fr_y = 1 (slider from 0 to 1, step 0.1)
Fg_y = 0 (slider from 0 to 1, step 0.1)
Fg_x = 1 (slider from 0 to 1, step 0.1)
Fb_x = 0 (slider from 0 to 1, step 0.1)
Fb_y = 0.1 (slider from 0 to 1, step 0.1)
Linienstärke = 5 (slider from 0 to 11, step 1)
Festlinien = false
rot = 0.1 (slider from 0 to 1, step 0.1)
grün = 0.9 (slider from 0 to 1, step 0.1)
blau = 0.1 (slider from 0 to 1, step 0.1)
Deckkraft = 0.12 (slider from 0 to 1, step 0.02)
Text15: "" + Text13 + ""
Text5: "$A_Z(x,y,t)-A_z=0⇔ " + (LaTeX[f]) + " = 0 $"

Tool: Ellipse
S1 S2 dd
Input: S_2, S_1, aΔEllipse
Output: ee4

L = Distance(S_1, S_2)
Sα = Angle(Line[S_1, S_2], xAxis)
ee4 = CurveCartesian((((-aΔEllipse) * cos(t)) * cos(Sα)) - ((sqrt((-(L / 2)^(2)) + aΔEllipse^(2)) * sin(t)) * sin(Sα)) + x(S_1 + S_2) / 2, ((aΔEllipse * cos(t)) * sin(Sα)) - ((sqrt((-(L / 2)^(2)) + aΔEllipse^(2)) * sin(t)) * cos(Sα)) + y(S_1 + S_2) / 2, t, -4.5, 4.5)

Tool: Hy
S1 S2 dd
Input: S_2, S_1, aΔHy
Output: ee3

L = Distance(S_1, S_2)
Sα = Angle(Line[S_1, S_2], xAxis)
ee3 = CurveCartesian((((-aΔHy) * cosh(t)) * cos(Sα)) - ((sqrt((L / 2)^(2) - aΔHy^(2)) * sinh(t)) * sin(Sα)) + x(S_1 + S_2) / 2, ((aΔHy * cosh(t)) * sin(Sα)) - ((sqrt((L / 2)^(2) - aΔHy^(2)) * sinh(t)) * cos(Sα)) + y(S_1 + S_2) / 2, t, -4.5, 4.5)