Two-dimensional standing wave on a disk
Author: Roman Chijner, Heidelberg
Date: 13 Dezember 2012

This animation refers to the archive:   https://www.geogebra.org/forum/viewtopic.php?f=52&t=20174

Two-dimensional standing wave on a disk

II←

v=\frac{\omega}{k}

k=\frac{2*pi}{\lambda}

StartAnimation

Roman Chijner, Heidelberg 2012

A_0 = 0.2 (slider from 0 to 5, step 0.1)
λ = 2 (slider from 0 to 15, step 0.1)
t = 0 (slider from 0 to 55, step 0.02)
v = 1.5 (slider from 0 to 5, step 0.1)
f = Function(A_0 * (cos(2 * π / λ * (sqrt(x^(2) + y^(2)) - v * t)) + cos(2 * π / λ * (sqrt(x^(2) + y^(2)) + v * t))), -2, 2, -2, 2)
A0: (0, 0, f(0, 0))
A1_1: (λ / 2, 0, f(λ / 2, 0))
A1_2: (0, λ / 2, f(0, λ / 2))
A1_4: ((-λ) / 2, 0, f((-λ) / 2, 0))
A1_3: (0, (-λ) / 2, f(0, (-λ) / 2))
Anode1 = Circle(A1_1, A1_2, A1_4)
A2_1: (λ, 0, f(λ, 0))
A2_2: (0, λ, f(0, λ))
A2_3: (-λ, 0, f(-λ, 0))
A2_4: (0, -λ, f(0, -λ))
Anode2 = Circle(A2_1, A2_2, A2_3)
B2_1: (3 * λ / 4, 0, f(3 * λ / 4, 0))
B2_2: (0, 3 * λ / 4, f(0, 3 * λ / 4))
B2_3: (-3 * λ / 4, 0, f(-3 * λ / 4, 0))
Node2 = Circle(B2_1, B2_2, B2_3)
B3_1: (5 * λ / 4, 0, f(5 * λ / 4, 0))
B3_2: (0, 5 * λ / 4, f(0, 5 * λ / 4))
B3_3: (-5 * λ / 4, 0, f(-5 * λ / 4, 0))
Node3 = Circle(B3_1, B3_2, B3_3)
b = false
B1_1: (λ / 4, 0, f(λ / 4, 0))
B1_2: (0, λ / 4, f(0, λ / 4))
B1_3: ((-λ) / 4, 0, f((-λ) / 4, 0))
Node1 = Circle(B1_1, B1_2, B1_3)
Text1: "f(x,y)=A_0 *cos(k r-ωt)+A_0 *cos(k r+ωt)=" + (LaTeX[f]) + ""
text2: "Node:
B1_1 = (λ / 4, 0, f(λ / 4, 0))=" + B1_1 + "
B2_1 = (3λ / 4, 0, f(3λ / 4, 0))=" + B2_1 + "
B3_1 = (5λ / 4, 0, f(5λ / 4, 0))=" + B3_1 + ""
text1: "Antinode:
A0 = (0, 0, f(0, 0))=" + A0 + "
A1_1 = (λ / 2, 0, f(λ / 2, 0))=" + A1_1 + "
A2_1 = (λ, 0, f(λ, 0))=" + A2_1 + ""