{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Waves and Stability\n",
"\n",
"Copyright (C) 2010-2020 Luke Olson \n",
"Copyright (C) 2020 Andreas Kloeckner\n",
"\n",
"\n",
"MIT License\n",
"Permission is hereby granted, free of charge, to any person obtaining a copy\n",
"of this software and associated documentation files (the \"Software\"), to deal\n",
"in the Software without restriction, including without limitation the rights\n",
"to use, copy, modify, merge, publish, distribute, sublicense, and/or sell\n",
"copies of the Software, and to permit persons to whom the Software is\n",
"furnished to do so, subject to the following conditions:\n",
"\n",
"The above copyright notice and this permission notice shall be included in\n",
"all copies or substantial portions of the Software.\n",
"\n",
"THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n",
"IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n",
"FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE\n",
"AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n",
"LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,\n",
"OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN\n",
"THE SOFTWARE.\n",
""
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Wavelength and Wavenumber\n",
"\n",
"Let $j$ be the wave number, then\n",
"$$\n",
"j = \\frac{2\\pi}{\\tilde{\\lambda}}\n",
"$$\n",
"where $\\tilde{\\lambda}$ is the wavelength.\n",
"\n",
"A sinusoidal wave is expressed as\n",
"$$\n",
"A \\cos \\left( \\frac{2 \\pi x}{\\tilde{\\lambda}} \\right).\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"[]"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
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