simOndeProgressive.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# La propagation d'une onde\n",
    "\n",
    "##  Spécialité Physique Chimie de première\n",
    "\n",
    "### Ludovic Gaudichet, lycée René Cassin, Noisiel\n",
    "\n",
    "###\n",
    "\n",
    "Capacités numériques : Représenter un signal périodique et illustrer l’influence de ses caractéristiques (période, amplitude) sur sa représentation. Simuler à l’aide d’un langage de programmation, la propagation d’une onde périodique.\n",
    "\n",
    " Capacité mathématique : Utiliser les représentations graphiques des fonctions sinus et cosinus."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exécuter ligne par ligne : >| ; Redémarrer et exécuter l'ensemble : >>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "from math import *\n",
    "from matplotlib import pyplot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Quelques paramètres du système\n",
    "C'est une corde tendue horizontalement."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "L = 20             # (m) longueur de la corde\n",
    "celerite = 8       # (m.s-1)\n",
    "duree = L/celerite # (s)\n",
    "# |-> temps mis par l'onde pour parcourir toute la corde"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Définition de la perturbation\n",
    "grâce à une fonction (du temps) qui donne l'amplitude à un certain temps. Dans le cas d'une corde tendue horizontalement, l'amplitude est en fait la hauteur d'un point de la corde.\n",
    "\n",
    "On va faire simple pour commencer, en imaginant qu'au début, l'extrémité de départ de la corde monte à 1 m, puis ce point descend progressivement à 0 m en 0,1 seconde. La fonction peut s'écrire ainsi :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Perturbation(temps):\n",
    "    # à la position (0,0)\n",
    "    # temps en seconde\n",
    "    # amplitude en mètre\n",
    "\n",
    "    amplitude = 0\n",
    "    if temps>=0 and temps<=0.1 :\n",
    "        amplitude = 1-temps*10\n",
    "    return amplitude"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Représentation temporelle de l'onde\n",
    "Comment évolue l'amplitude au point de départ de l'onde (x=0) ? Il s'agit simplement de tracer le graphe en fonction du temps de la fonction précédente."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "D'abord on créé une liste de coordonnées temporelles, puis les amplitudes correspondantes :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "Np = 200 # nbre de points\n",
    "dt = duree/Np\n",
    "list_t = [] # temps\n",
    "list_a = [] # amplitude\n",
    "\n",
    "for i in range (0,Np-1):\n",
    "    temps = i*dt\n",
    "    list_t.append(temps)\n",
    "    list_a.append( Perturbation(temps) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Puis on trace le graphe :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f5e4eb46ed0>]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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fZrDfzO1oGSduWOUr3M3M6iHPFslx6d+TM+MC2KP24dTe1hNa2HsX3wnYzKxeBi0kEbF7IwKpp3lzWrnghtVs2RKMG6eywzEzG1UGutfWPw70wvRK9/1qH1LtdbRtz2ObNnPXgz1lh2JmNuoMdIzkdZL+KOlTkv5Z0kGSXizpHZLOAS4Cti6ycEkvl3S7pBWSTqoyvVPSo5KWpt2nhrOcjt4LE717y8ys5vrdtRURH5K0PfB64A0kd//dCCwHTouIq4ssWFIL8G3gCKAbuE7Sooi4taLpVRHxyiLL2mPaZKZOGs8N963njQe2FZmVmZlVGPAYSUQ8ApyedrV2ELAiIu4GkPRT4GigspAUNm6c6GjznYDNzOqhzCckzgJWZYa703GVDpF0o6RLJO073IV1tLVy+/0beOKpzcOdhZmZVZHn9N96qXb6VOUD1pcAu0ZEj6T5wK+AuVVnJi0AFgBMnz6drq6uZ0xvWb+ZLQHnXPR72ndoKRp70+jp6XlWLsYi56GPc9HHuaiNMgtJN5A9YDEbWJ1tEBEbMv2LJX1H0rRqdyKOiIXAQoD29vbo7Ox8xvTn9Wzia0sugx13o/Mle9buXYxwXV1dVOZiLHIe+jgXfZyL2sjzPJJtJH1S0unp8FxJhQ5+p64D5kraXdIE4BhgUcWyd5GktP+gNN51w1nYjlMmMmeHbbjhPh8nMTOrpTxbJN8neZjVIelwN/BzktN/hy0iNkt6H8kz4VuAMyNimaR3p9NPJTlj7D2SNpOcMXZMRFTu/sqto62VP698uEjYZmZWIU8h2TMi3iTpWICI2Ni7lVBURCwGFleMOzXT/y3gW7VYFiSFZNGNq7n/0SfZZbtJtZqtmdmYluesrackbU16IFzSnmSeS9JM5vXeCdg3cDQzq5k8heQU4NdAm6QfAZcDH6trVHWyz8xtmdAyzle4m5nVUJ6bNv5W0hLgYJJTdj/QjM9vB5g4voXnztzWB9zNzGqo30Iiaf+KUWvSv3MkzYmIJfULq37mtbXys+tWsfnpLYxvKfN6TDOz0WGgLZIvp38nAQcCN5JskTwfuBYY8O7AI1VHWytn/fEe7nigh31mblt2OGZmTa/fn+QRcVhEHAbcC+wfEQdGxAHAPGBFowKstb4D7t69ZWZWC3n27ewdETf3DkTELUBH/UKqrzk7bMMOkyf4zC0zsxrJcx3JcknfA35IcgrwW0huJd+UJPGC2dv5gLuZWY3k2SI5AVgGfAD4IMlt3k+oZ1D11tG2PSse7OGxJ/9WdihmZk0vz+m/TwJfTbtRoWNOKxFwU/ejHLrXtLLDMTNraoMWEkkrefbt3YmIPeoSUQN0zO474O5CYmZWTJ5jJAdm+ieRPHZ3h/qE0xjbbbMVe0yf7OMkZmY1MOgxkohYl+n+GhFfA17agNjqKnn07iMUuJmwmZmRb9dW9gr3cSRbKFPrFlGDzGtr5ZdL/kr3Ixtp22GbssMxM2taeXZtfTnTvxlYCbyxPuE0Tkfb9kBynMSFxMxs+PIUkv8fEXdnR0javU7xNMzeM6Yycfw4lq5az1EvmFl2OGZmTSvPdSS/yDmuqWzVMo7nzdrOt0oxMytooLv/7g3sC2wn6bWZSduSnL3V9DraWjnnmnt5avMWJoz3nYDNzIZjoG/PduCVQCtwVKbbH3hX/UOrv445rWzavIXb7t9QdihmZk2r3y2SiLgAuEDSIRHxpwbG1DAdbX0XJj4/vUjRzMyGZqBdWx+LiP8BjpN0bOX0iHh/XSNrgFmtWzNtykSW3ree4w8pOxozs+Y00FlbvXf4vb4RgZRBUnphog+4m5kN10C7ti5M//6gXguX9HLg60AL8L2I+GLFdKXT5wNPAG+v9SN+581p5bLlD7D+iado3WZCLWdtZjYmDLRr60Kq3KyxV0S8qsiCJbUA3waOALqB6yQtiohbM81eAcxNuxcC303/1sy8zHGSzvadajlrM7MxYaBdW1+q87IPAlb0Xuwo6afA0STPO+l1NHB2JDfEukZSq6QZEbGmVkE8b/Z2SHDVnQ+x+7TJtZrtiLH2iS3cu+7xssMonfPQx7noM9ZzMWH8OGZst3Xh+Qy0a+v3vf2SJgB7k2yh3B4RTxVeMswCVmWGu3n21ka1NrOAmhWSqZO2on3nqZxx9UrOuHplrWY7slzZVXYEI4Pz0Me56DOGczFvTivnv/fQwvPJc9PGfwZOBe4CBOwu6V8i4pKCy1aVcZW70vK0SRpKC4AFANOnT6erqyt3IMfvtYWV00fn8ZFNmzYxceLEssMonfPQx7noM9ZzMXXCxiF9V/Yn700bD4uIFQCS9gQuBooWkm6gLTM8G1g9jDYARMRCYCFAe3t7dHZ2FgxvdOjq6sK5cB6ynIs+zkVt5LkvyNreIpK6G1hbg2VfB8yVtHu66+wYYFFFm0XA8UocDDxay+MjZmZWXJ4tkmWSFgPnkuxWegPJGVavBYiIXw5nwRGxWdL7gEtJTv89MyKWSXp3Ov1UYDHJqb8rSE7/PWE4yzIzs/rJU0gmAQ8AL0mHHyR51O5RJIVlWIUEICIWkxSL7LhTM/0BnDjc+ZuZWf0NWkgiwlsBZmbWrzxnbe0O/CuwW7Z90QsSzcxsdMiza+tXwBnAhcCW+oZjZmbNJk8heTIivlH3SMzMrCnlKSRfl3QK8BtgU+/IWt880czMmlOeQvI84K3AS+nbtRXpsJmZjXF5CslrgD1qdH8tMzMbZfJc2X4jyXPbzczMniXPFsnOwG2SruOZx0h8+q+ZmeUqJKfUPQozM2taea5s/312WNKhwHHA76u/wszMxpI8WyRI6iApHm8EVgLn1TMoMzNrHgM9s/05JLd2PxZYB/wMUEQc1qDYzMysCQy0RXIbcBVwVOahVh9qSFRmZtY0Bjr993XA/cAVkk6X9E9Uf/StmZmNYf0Wkog4PyLeBOwNdAEfAnaW9F1JRzYoPjMzG+EGvSAxIh6PiB9FxCtJnpm+FDip7pGZmVlTyHNl+99FxMMRcVpE+D5bZmYGDLGQmJmZVXIhMTOzQlxIzMysEBcSMzMrxIXEzMwKyXWvrVqTtAPJLVd2A+4B3hgRj1Rpdw/wGPA0sDkiDmxclGZmlkdZWyQnAZdHxFzgcga+LuWwiOhwETEzG5nKKiRHAz9I+38AvLqkOMzMrCBFROMXKq2PiNbM8CMRsX2VdiuBR4AATouIhQPMcwGwAGD69OkHnHvuubUPvAn19PQwZcqUssMonfPQx7no41z0Oeyww/4y3D0/dTtGIukyYJcqkz4xhNkcGhGrJe0E/FbSbRFxZbWGaZFZCNDe3h6dnZ1DDXlU6urqwrlwHrKciz7ORW3UrZBExOH9TZP0gKQZEbFG0gxgbT/zWJ3+XSvpfOAgoGohMTOzcpR1jGQR8La0/23ABZUNJE2WNLW3HzgSuKVhEZqZWS5lFZIvAkdIuhM4Ih1G0kxJi9M2OwNXS7oR+DNwcUT8upRozcysX6VcRxIR64B/qjJ+NTA/7b8beEGDQzMzsyHyle1mZlaIC4mZmRXiQmJmZoW4kJiZWSEuJGZmVogLiZmZFeJCYmZmhbiQmJlZIS4kZmZWiAuJmZkV4kJiZmaFuJCYmVkhLiRmZlaIC4mZmRXiQmJmZoW4kJiZWSEuJGZmVogLiZmZFeJCYmZmhbiQmJlZIS4kZmZWiAuJmZkVUkohkfQGScskbZF04ADtXi7pdkkrJJ3UyBjNzCyfsrZIbgFeC1zZXwNJLcC3gVcA+wDHStqnMeGZmVle48tYaEQsB5A0ULODgBURcXfa9qfA0cCtdQ/QzMxyK6WQ5DQLWJUZ7gZe2F9jSQuABQDTp0+nq6urrsE1i56eHucC5yHLuejjXNRG3QqJpMuAXapM+kREXJBnFlXGRX+NI2IhsBCgvb09Ojs784Q56nV1deFcOA9ZzkUf56I26lZIIuLwgrPoBtoyw7OB1QXnaWZmNTaST/+9DpgraXdJE4BjgEUlx2RmZhXKOv33NZK6gUOAiyVdmo6fKWkxQERsBt4HXAosB86NiGVlxGtmZv0r66yt84Hzq4xfDczPDC8GFjcwNDMzG6KRvGvLzMyagAuJmZkV4kJiZmaFuJCYmVkhLiRmZlaIC4mZmRXiQmJmZoW4kJiZWSEuJGZmVogLiZmZFeJCYmZmhbiQmJlZIS4kZmZWiAuJmZkV4kJiZmaFuJCYmVkhLiRmZlaIC4mZmRXiQmJmZoW4kJiZWSEuJGZmVogLiZmZFVJKIZH0BknLJG2RdOAA7e6RdLOkpZKub2SMZmaWz/iSlnsL8FrgtBxtD4uIh+ocj5mZDVMphSQilgNIKmPxZmZWQ2VtkeQVwG8kBXBaRCzsr6GkBcCCdHCTpFsaEWATmAZ4i855yHIu+jgXfdqH+8K6FRJJlwG7VJn0iYi4IOdsDo2I1ZJ2An4r6baIuLJaw7TILEyXfX1E9HvsZSxxLhLOQx/noo9z0afIcei6FZKIOLwG81id/l0r6XzgIKBqITEzs3KM2NN/JU2WNLW3HziS5CC9mZmNIGWd/vsaSd3AIcDFki5Nx8+UtDhttjNwtaQbgT8DF0fEr3Muot9jKWOQc5FwHvo4F32ciz7DzoUiopaBmJnZGDNid22ZmVlzcCExM7NCmraQSHq5pNslrZB0UpXpkvSNdPpNkvYvI85GyJGLTkmPpreaWSrpU2XE2QiSzpS0tr/riMbYejFYLsbEeiGpTdIVkpant2b6QJU2Y2K9yJmLoa8XEdF0HdAC3AXsAUwAbgT2qWgzH7gEEHAwcG3ZcZeYi07gorJjbVA+XgzsD9zSz/QxsV7kzMWYWC+AGcD+af9U4I4x/H2RJxdDXi+adYvkIGBFRNwdEU8BPwWOrmhzNHB2JK4BWiXNaHSgDZAnF2NGJBesPjxAk7GyXuTJxZgQEWsiYkna/xiwHJhV0WxMrBc5czFkzVpIZgGrMsPdPDsZedqMBnnf5yGSbpR0iaR9GxPaiDRW1ou8xtR6IWk3YB5wbcWkMbdeDJALGOJ6MdLvtdWfand7rDyPOU+b0SDP+1wC7BoRPZLmA78C5tY9spFprKwXeYyp9ULSFOA84IMRsaFycpWXjNr1YpBcDHm9aNYtkm6gLTM8G1g9jDajwaDvMyI2RERP2r8Y2ErStMaFOKKMlfViUGNpvZC0FckX548i4pdVmoyZ9WKwXAxnvWjWQnIdMFfS7pImAMcAiyraLAKOT8/GOBh4NCLWNDrQBhg0F5J2UXrPfkkHkXzu6xoe6cgwVtaLQY2V9SJ9j2cAyyPiK/00GxPrRZ5cDGe9aMpdWxGxWdL7gEtJzlo6MyKWSXp3Ov1UYDHJmRgrgCeAE8qKt55y5uL1wHskbQY2AsdEenrGaCPpJyRnnUxTchueU4CtYGytF5ArF2NlvTgUeCtws6Sl6biPA3NgzK0XeXIx5PXCt0gxM7NCmnXXlpmZjRAuJGZmVogLiZmZFeJCYmZmhbiQmJlZIS4kZhmSWiW9t+w4ekn6haQ9Bpj+JUkvbWRMZpVcSMyeqRUYEYUkvcdRS0TcPUCzbwLPenSAWSO5kJg90xeBPdPnMPwvgKSPSroufU7Ff6bjdpN0m6TvSbpF0o8kHS7pD5LuTK8IRtKnJZ0j6Xfp+Hel42dIujJdzi2SXlQlljcDF6TtWySdlba9WdKHACLiXmBHSbvUPzVm1TXlle1mdXQSsF9EdABIOpLkhnUHkdzYb5GkFwP3AXsBbwAWkNyq5jjgH4FXkVwt/Op0ns8necbFZOAGSRcDxwKXRsTnJLUA21SJ5VDgJ2l/BzArIvZL42rNtFuStj2v8Ls3GwYXErOBHZl2N6TDU0gKy33Ayoi4GUDSMuDyiAhJNwO7ZeZxQURsBDZKuoKkKF0HnJneQO9XEbGUZ5sBPJj23w3sIembwMXAbzLt1gIzC79Ts2Hyri2zgQn4QkR0pN1eEXFGOm1Tpt2WzPAWnvkjrfI+RJE+dOrFwF+BcyQdX2XZG4FJ6QseAV4AdAEnAt/LtJuUtjUrhQuJ2TM9RvII0l6XAu9In9+ApFmSdhriPI+WNEnSjiQ3UbxO0q7A2og4neRurNWeEb6cZPcZ6W28x0XEecAnK9o/B1aJ/MsAAAC9SURBVKj6XHazRvCuLbOMiFiXHjC/BbgkIj4q6bnAn9I7a/cAbwGeHsJs/0yyO2oO8F8RsVrS24CPSvpbOs9qWyQXkxSey0ie1vd9Sb0//k6Gvz9bYi/g+qG9U7Pa8d1/zepI0qeBnoj40jBeuzVwBXBoRFQtXJJeA+wfEZ8sFKhZAd61ZTZCpQfoT2HgZ4ePB77cmIjMqvMWiZmZFeItEjMzK8SFxMzMCnEhMTOzQlxIzMysEBcSMzMr5P8AUtAB29kbLsQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pyplot.close()\n",
    "#fig, ax = pyplot.subplots(1,1,figsize=(6,7))\n",
    "fig, ax = pyplot.subplots(1,1)\n",
    "ax.grid(True)\n",
    "ax.axis([0,duree, -1.5, 2])\n",
    "ax.set_xlabel('temps (s)')\n",
    "ax.set_ylabel('Amplitude (m)')\n",
    "ax.set_title(\"Représentation temporelle en x = 0 m\")\n",
    "ax.plot(list_t, list_a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Représentation temporelle en un autre point\n",
    "\n",
    "Comment peut-on montrer l'amplitude de la corde en n'importe quel autre point de la corde, en fonction du temps ?\n",
    "On peut considérer qu'en ce point, la perturbation sera la même, mais avec un certain retard, dû au temps de propagation.\n",
    "Il suffit donc d'introduire ce retard quand on utilise la fonction Perturbation() (qui reste la même donc)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "mon_x = 5.3 # à x m du point de départ de la perturbation\n",
    "retard = mon_x/celerite\n",
    "\n",
    "for i in range (0,Np-1):\n",
    "    temps = i*dt\n",
    "    list_t[i] = temps\n",
    "    list_a[i] = Perturbation(temps-retard)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Remarque : Les listes sont déjà créées, on les réutilise.\n",
    "\n",
    "Ensuite on trace le graphe :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f5e4ea81cd0>]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = pyplot.subplots(1,1)\n",
    "ax.grid(True)\n",
    "ax.axis([0,duree, -1.5, 2])\n",
    "ax.set_xlabel('temps (s)')\n",
    "ax.set_ylabel('Amplitude (m)')\n",
    "ax.set_title(\"Représentation temporelle de la perturbation en x=\"\n",
    "        + format(mon_x,'.1f') + \" m\")\n",
    "ax.plot(list_t, list_a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Représentation spatiale de l'onde\n",
    "\n",
    "Grâce à cette expression Perturbation(temps-retard), on peut maintenant savoir l'amplitude de l'onde, n'importe quand et n'importe où.\n",
    "\n",
    "Cela permet de tracer la représentation spatiale de l'onde, c'est-à-dire son allure si on la prenait en photo à un certain temps.\n",
    "Il suffit de faire une liste de coordonnées (spatiales) et la liste des amplitudes qui correspondent :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "mon_t = 1.5 # après t secondes\n",
    "\n",
    "list_x = [] # x des points\n",
    "\n",
    "for i in range (0,Np-1):\n",
    "\n",
    "    coord_x = L*i/Np\n",
    "    list_x.append(coord_x)\n",
    "\n",
    "    retard = coord_x/celerite\n",
    "    list_a[i] = Perturbation(mon_t - retard)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ensuite, on trace :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f5e4eaadd50>]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = pyplot.subplots(1,1)\n",
    "ax.grid(True)\n",
    "ax.axis([0,L, -1.5, 2])\n",
    "ax.set_xlabel('x (m)')\n",
    "ax.set_ylabel('Amplitude (m)')\n",
    "ax.set_title(\"Représentation spatiale de la perturbation à t =\"\n",
    "        + format(mon_t,'.1f') + \" s\")\n",
    "ax.plot(list_x, list_a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Je vous laisse méditer très profondément sur pourquoi la représentation spatiale ressemble à la représentation temporelle, mais à l'envers."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Perturbation sinusoïdale\n",
    "\n",
    "Imaginons maintenant que la pertubation est sinusoïdale : un opérateur monte et descend la corde périodiquement (apparemment c'est même un sport qui se pratique avec de grosses cordes).\n",
    "Ce mouvement est en fait beaucoup plus simple physiquement que la première perturbation (qui est en fait impossible à vraiment réaliser).\n",
    "La fonction correspondante est la suivante :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def PerturbSinus(temps):\n",
    "    # à la position (0,0)\n",
    "    # temps en seconde\n",
    "    # amplitude en mètre\n",
    "\n",
    "    T = 0.5 # période en s\n",
    "    amplitude = 1.*sin(temps*2*pi/T)\n",
    "    \n",
    "    if temps>0.15 and temps<=0.20:\n",
    "        amplitude = 0.6\n",
    "\n",
    "    return amplitude"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La fonction $sinus(x)$ est utilisée avec la variable :\n",
    "$x = temps \\times {2\\pi \\over T}$\n",
    "\n",
    "$x$ varie alors de $0$ à $2\\pi$ quand le temps varie de $0$ à une période $T$.\n",
    "\n",
    "Cette fonction produit donc bien une amplitude qui varie sinusoïdalement avec une période T.\n",
    "\n",
    "La partie :\n",
    "\n",
    " if temps>0.15 and temps<=0.20:\n",
    "        amplitude = 0.6\n",
    "\n",
    "permet d'introduire un petite distorsion dans la corde pour mieux visualiser la propagation de l'onde. Observons le mouvement de l'extrémité de la corde en fonction du temps :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f5e4e978f10>]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mon_x = 0 # à x m du point de départ de la perturbation\n",
    "retard = mon_x/celerite\n",
    "\n",
    "for i in range (0,Np-1):\n",
    "    temps = i*dt\n",
    "    list_a[i] = PerturbSinus(temps-retard)\n",
    "    \n",
    "fig, ax = pyplot.subplots(1,1)\n",
    "ax.grid(True)\n",
    "ax.axis([0,duree, -1.5, 2])\n",
    "ax.set_xlabel('temps (s)')\n",
    "ax.set_ylabel('Amplitude (m)')\n",
    "ax.set_title(\"Amplitude de la corde en x=\"\n",
    "        + format(mon_x,'.1f') + \" m\")\n",
    "ax.plot(list_t, list_a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Remplissons la liste des x avec la hauteur des points de la corde quand la perturbation est sinusoïdale, puis affichons la représentation spatiale correspondante."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "mon_t = 0.5 # après t secondes\n",
    "\n",
    "for i in range (0,Np-1):\n",
    "    \n",
    "    coord_x = L*i/Np\n",
    "    retard = coord_x/celerite\n",
    "    list_a[i] = PerturbSinus(mon_t - retard)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f5e4e96d8d0>]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = pyplot.subplots(1,1)\n",
    "ax.grid(True)\n",
    "ax.axis([0,L, -1.5, 2])\n",
    "ax.set_xlabel('x (m)')\n",
    "ax.set_ylabel('Amplitude (m)')\n",
    "ax.set_title(\"Représentation spatiale à t =\"\n",
    "        + format(mon_t,'.1f') + \" s\")\n",
    "ax.plot(list_x, list_a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Comme exercice, vous pouvez changer la valeurs du temps et relancer les deux dernières parties de code. Vérifiez ainsi que cette onde se propage, notamment par le déplacement de la distorsion. Déterminez approximativement la valeur de la célérité grâce à vos essais."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "x =3\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3\n"
     ]
    }
   ],
   "source": [
    "print(x)"
   ]
  },
  {
   "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": "3.8.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}