{
"cells": [
{
"cell_type": "markdown",
"id": "4da58ef7-37db-460b-acf5-cd7e342a89a8",
"metadata": {
"tags": []
},
"source": [
"# Kahden harmonisen aallon superposition aikakehitys.\n",
"\n",
"Alustellaan aluksi juttuja."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "adfd5691-b196-4c28-a98e-15b521152afa",
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import numpy as np\n",
"from matplotlib import pyplot as plt\n",
"from matplotlib import animation, rc\n",
"from IPython.display import HTML\n",
"\n",
"plt.rcParams['text.usetex'] = True\n",
"\n",
"L = 100.0\n",
"xvals = np.linspace(-L/2,L/2,10000)"
]
},
{
"cell_type": "markdown",
"id": "1624c1d1-2633-4fd8-bd81-a230c0b17725",
"metadata": {},
"source": [
"Määritellään aikakehitysfunktio evolve. Se koostuu suoraan kahdesta oikealle etenevästä harmonisesta aallosta. Dispersiota voi muokata muuttamalla esimerkiksi kulmataajuutta."
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "81714ed8-8746-45b1-8efb-ed3d52944b49",
"metadata": {},
"outputs": [],
"source": [
"def evolve(xvals,time):\n",
" yt = [np.cos(1.0*x-0.25*time) + np.cos(1.2*x-0.27*time) for x in xvals]\n",
" return yt"
]
},
{
"cell_type": "markdown",
"id": "02050c0f-af23-431b-84b7-c4f7d2e10d0a",
"metadata": {},
"source": [
"Ja sitten varsinainen animointi."
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "c7e7976d-3459-42ad-a915-d34a3abd5826",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
""
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots()\n",
"ax.set_xlim(-L/2,L/2)\n",
"ax.set_ylim(-2.0,2.0)\n",
"\n",
"line, = ax.plot([])\n",
"\n",
"def init():\n",
" line.set_data([], [])\n",
" return (line,)\n",
"\n",
"def animate(frame_num):\n",
" ynew = evolve(xvals,frame_num*1.0)\n",
" line.set_data(xvals,ynew)\n",
" return (line,)\n",
"\n",
"anim = animation.FuncAnimation(fig,animate,init_func=init,frames=100,interval=100)\n",
"HTML(anim.to_html5_video())"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "0be82db8-bcf6-4ad2-be6d-802ab82a54a0",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.9.5"
}
},
"nbformat": 4,
"nbformat_minor": 5
}