{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Wave Propagation\n",
    "\n",
    "\n",
    "A wave function is defined as \n",
    "\n",
    "$Y = A \\sin(\\omega t + kx)$\n",
    "\n",
    "Differential equation\n",
    "\n",
    "$\\large{\\frac{\\partial^{2}U}{dt^{2}} = c^{2}\\frac{\\partial^{2}U}{dx^{2}}}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns \n",
    "sns.set()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Define Amplitude, angular frequency, wave vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "amp = 1.0\n",
    "freq = 1\n",
    "w = 2*np.pi*freq #angular frequency\n",
    "k = 2*np.pi #wave vector"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Calcualte frequency, weblength and velocity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1, 1.0, 1.0)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wave_length = 2*np.pi/k\n",
    "velocity = freq*wave_length\n",
    "(freq,wave_length,velocity)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot the different configuration of wave motion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "xs = np.arange(0,5,1/20)\n",
    "ts = np.arange(0,5,1/20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 100)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(xs),len(ts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. Experiment: Plot the particle displacement keeping time fixed\n",
    "When we fix the time, it is a photograph of the wave motion at specific time t0. It can be represent as\n",
    "\n",
    "$Y = A \\sin (kx + \\phi_{0})$\n",
    "\n",
    "A special case is **closed vibrating string**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Particle displacements at t=0.0')"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x144 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = [18,2])\n",
    "t0 = 0.0\n",
    "y = amp*np.sin(w*t0 - k*xs)\n",
    "plt.stem(y)\n",
    "plt.xlabel(\"Distance\")\n",
    "plt.ylabel(\"Amplitude\")\n",
    "plt.title('Particle displacements at t=' + str(t0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x1296 with 5 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = [18,18])\n",
    "t0s = [0.0,0.1,0.2,0.3,0.4]\n",
    "for i,t0 in enumerate(t0s):\n",
    "    plt.subplot(len(t0s),1,i+1)\n",
    "    y = amp*np.sin(w*t0 - k*xs)\n",
    "    plt.stem(y)\n",
    "    plt.title('Particle displacements at t=' + str(t0))\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. Experiment: Plot the particle displacement keeping position fixed\n",
    "\n",
    "When we fix the position and look at a single particle displacement, it behaves like a harmonic oscillator. It can be represent as\n",
    "\n",
    "$Y = A \\sin (\\omega t + \\phi_{0})$\n",
    "\n",
    "A special case is **harmonic oscillator**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Particle motion at x=0.0')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x144 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = [18,2])\n",
    "x0 = 0.0\n",
    "y = amp*np.sin(w*ts - k*x0)\n",
    "plt.stem(y)\n",
    "plt.xlabel(\"Time\")\n",
    "plt.ylabel(\"Amplitude\")\n",
    "plt.title(\"Particle motion at x=\" + str(x0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x1296 with 5 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = [18,18])\n",
    "x0s = [0.0,0.1,0.2,0.3,0.4]\n",
    "for i,x0 in enumerate(t0s):\n",
    "    plt.subplot(len(x0s),1,i+1)\n",
    "    y = amp*np.sin(w*ts - k*x0)\n",
    "    plt.stem(y)\n",
    "    plt.title('Particle displacements at x=' + str(x0))\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "-----------------"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Animation 1D\n",
    "\n",
    "Wave propagation in 1D\n",
    "\n",
    "![img](plot/wave.gif)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Next Step: \n",
    "Wave Propagation in 2D (```numpy meshgrid```)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"https://upload.wikimedia.org/wikipedia/commons/b/bb/2D_Wave_Function_resize.gif\" width=\"250\" height =\"300\"> </img>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}