{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "The goal of this notebook is to implement a simple 1D wave propagation simulation, as explained by Hans-Petter Langtangen in his class [INF5620](https://github.com/hplgit/INF5620) and more precisely in [this PDF](hplgit.github.io/INF5620/doc/pub/main_wave.pdf). The problem to be solved is that of a wave propagating on a string, just like in the case of a guitar.\n", "\n", "In this notebook, we will use the simulation code writte by Mr Langtangen for the case of a (transversely) vibrating string and perform extractions of the simulated date so as to visualize it. In this process, we will use Matplotlib to embed animations and perform a little bit of Fourier analysis.\n", "\n", "First, let's simulate the string!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Simulation " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Below, I've adapted the code of Mr Langtangen (from the above cited PDF)." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from numpy import linspace, zeros\n", "\n", "def solver(I, V, f, c, L, Nx, C, T, user_action=None):\n", " \"\"\"Solve u_tt=c^2*u_xx + f on (0,L)x(0,T].\"\"\"\n", " x = linspace(0, L, Nx+1) # Mesh points in space\n", " dx = x[1] - x[0]\n", " dt = C*dx/c\n", " Nt = int(round(T/dt))\n", " t = linspace(0, Nt*dt, Nt+1) # Mesh points in time\n", " C2 = C**2 # Help variable in the scheme\n", " \n", " if f is None or f == 0 :\n", " f = lambda x, t: 0\n", " \n", " if V is None or V == 0:\n", " V = lambda x: 0\n", " u = zeros(Nx+1) # Solution array at new time level\n", " u_1 = zeros(Nx+1) # Solution at 1 time level back\n", " u_2 = zeros(Nx+1) # Solution at 2 time levels back\n", " \n", " import time; t0 = time.clock() # for measuring CPU time\n", " \n", " # Load initial condition into u_1\n", " for i in range(0,Nx+1):\n", " u_1[i] = I(x[i])\n", " if user_action is not None:\n", " user_action(u_1, x, t, 0)\n", " \n", " # Special formula for first time step\n", " n = 0\n", " for i in range(1, Nx):\n", " u[i] = u_1[i] + dt*V(x[i]) + \\\n", " 0.5*C2*(u_1[i-1] - 2*u_1[i] + u_1[i+1]) + \\\n", " 0.5*dt**2*f(x[i], t[n])\n", " u[0] = 0; u[Nx] = 0\n", " \n", " if user_action is not None:\n", " user_action(u, x, t, 1)\n", " \n", " # Switch variables before next step\n", " u_2[:], u_1[:] = u_1, u\n", " \n", " for n in range(1, Nt):\n", " # Update all inner points at time t[n+1]\n", " for i in range(1, Nx):\n", " u[i] = - u_2[i] + 2*u_1[i] + \\\n", " C2*(u_1[i-1] - 2*u_1[i] + u_1[i+1]) + \\\n", " dt**2*f(x[i], t[n])\n", " # Insert boundary conditions\n", " u[0] = 0; u[Nx] = 0\n", " if user_action is not None:\n", " if user_action(u, x, t, n+1):\n", " break\n", " # Switch variables before next step\n", " u_2[:], u_1[:] = u_1, u\n", " cpu_time = t0 - time.clock()\n", " return u, x, t, cpu_time" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The code calls a user defined routined at each simulation step.\n", "\n", "We can use that mechanism and define a user action routine that will store the simulation snapshots, so that we can perform some later analysis." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def user_action(u, x, t, n):\n", " \"Defines a user action that stores the current simulated state for further usage.\"\n", " global user_data\n", " if 'x' not in user_data:\n", " user_data['x'] = x\n", " if 'u' not in user_data:\n", " user_data['u'] = [(n, u)]\n", " else:\n", " user_data['u'].append((t[n], u.copy()))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's now run a simulation using initial conditions of a 1 meter long string in the shape of a quadratic function, for a duration of 1 second and a speed of sound of 100 m/s. At each time step, we keep the simulation state for later use." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "user_data = {}\n", "u, x, t, cpu_time = solver(lambda x: x*(1-x), None, None, 100, 1, 100, 0.1, 1., user_action=user_action)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Visualization of the data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now that we have gathered our date, let's start visualizing it. We can plot the final position of the string computed by the program:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "plt.style.use('bmh')" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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X1cyvNhy3e0gqCCG9mYuILAduBYbclDtw4AB33XUXJSUlAGRnZzNnzpy+/l7vb/t42F66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\nf6WUikP/Hx1Znl6KAIbPAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(x, u)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's examine the different simulation solution steps using a widget browser:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from ipywidgets import interact" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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ZwCQgG9gPrAUWqerK3pzURKaNe+u48/USdtY0khAnXHxsAV85Jt8a7CZijc1L4/5zj+RJ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\nCngXOMLTs7mkqze0nonLxoQ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "@interact\n", "def browse_simulation_result(n=(0, len(user_data['u']) - 1)):\n", " \"Plots a frame of the simulation.\"\n", " x = user_data['x']\n", " t, u = user_data['u'][n]\n", " plt.plot(x, u)\n", " plt.title('t = {:.2f}'.format(t))\n", " plt.ylim(-0.25, 0.25)\n", " plt.xlabel('x (a. u.)')\n", " plt.ylabel('vertical displacement (a. u.)')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see the string oscillating and keeping its initial bell shape. On the edges of the string, the zero displacement boundary condition keeps it fixed." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Animation of the data " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's now make a moviepy animation using this data. We can embed it directly in this notebook using the `ipython_display` function. " ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "WARNING:py.warnings:C:\\Anaconda3\\lib\\site-packages\\skimage\\filter\\__init__.py:6: skimage_deprecation: The `skimage.filter` module has been renamed to `skimage.filters`. This placeholder module will be removed in v0.13.\n", " warn(skimage_deprecation('The `skimage.filter` module has been renamed '\n", "\n", "100%|███████████████████████████████████████▉| 750/751 [00:51<00:00, 14.91it/s]\n" ] }, { "data": { "text/html": [ "
" ], "text/plain": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from moviepy.video.io.bindings import mplfig_to_npimage\n", "import moviepy.editor as mpy\n", "\n", "duration = 30\n", "\n", "fig, ax = plt.subplots(figsize=(4, 3), facecolor='white', dpi=150)\n", "plt.tight_layout()\n", "def make_frame_mpl(t):\n", " n = int(t / duration * (len(user_data['u']) - 1))\n", " ax.clear()\n", " x = user_data['x']\n", " t, u = user_data['u'][n]\n", " ax.plot(x, u)\n", " ax.set_title('t = {:.2f}'.format(t))\n", " ax.set_ylim(-0.25, 0.25)\n", " ax.set_xlabel('x (a. u.)')\n", " ax.set_ylabel('vertical displacement (a. u.)')\n", " return mplfig_to_npimage(fig) # RGB image of the figure\n", "\n", "animation = mpy.VideoClip(make_frame_mpl, duration=duration)\n", "plt.close(fig)\n", "animation.ipython_display(fps=25, width=800)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Looking at the spectrum of the data " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also build a matrix with some snapshots of the numerical solution. " ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": true }, "outputs": [], "source": [ "mat = np.array([b for a,b in user_data['u'][::20]])" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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ze5JYTbRLaVLcX+O4S8MqOGvT+IwFVvH52q8pw81OP05e86Q6ez+ff21fiDjn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\nFD3aej9NNSDK1SQ5Lfn0OY3Jk0KOs7rwNRQiXW/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DvnVZBahksQ3E7xI4EGsI63QhACJL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\nEeamAjFuyhPmphJZLpDkJHqXg8EScpJc8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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(mat, aspect='auto', cmap='magma')\n", "plt.xlabel('space dimension')\n", "plt.ylabel('time dimension')\n", "plt.colorbar()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As we can see on the above plot, we see the oscillations along the time dimension, as well as an amplitude that depends on the node location along the string (maximum in the center, zero on the edges)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can examine individual profiles of movement along the time dimension by performing vertical cuts in the above data:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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GNcIYRZRiGscqEYyliKviXpW2luem1QJGMVdVaagZPS6oVgRTZR6t99VYfJto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\npwv3Lpkb1Tg+uTaTs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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "@interact \n", "def space_cut(n=(0, mat.shape[1] - 1)):\n", " \"Plots time profile at fixed position.\"\n", " plt.plot(mat[:, n])\n", " plt.xlabel('time (a. u.)')\n", " plt.ylabel('amplitude (a. u.)')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can display these oscillations in time at different positions:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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cmkBJaNL5SQFM0mO/o1F7vFifNrhhvhctjbQXuZ0mg5mcmvAzosSzSs4jIk/UyaV/I54x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mW3qlZIR9mOHkvXLb2K0zMZjPkuOFvYscu2Z9r15QyJrTtQRQV/t9TZAoggN1MslXUCUiyVvLDn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\n7qawzlnbyXuNGHsWSis5s5Ztxa3l5yKMb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FxVfcA7phcYU9VTItIGfAv4kqo+Mw0mG4Zh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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "space_cut(1)\n", "space_cut(25)\n", "space_cut(49)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "What we see here is that depending on the observation location, the vibration profile looks similar, except for the amplitude: the edges of the string vibrate less than the middle of the string." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also perform a Fourier analysis of each slice:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [], "source": [ "dt = 20 * user_data['u'][1][0] - user_data['u'][0][0]" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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ww8GCiZUUFQi7TvQk/bX/2hHLDeXsPzHLdk/tTNIjyutvdZTE1JpSyooKiBgr\nKyoTuWxulIu7KZfaisEsWoY4sogLdmfpCvOd3ZRH59xsFUy24zt6BzP64SNRw22rtnDr/VuyvPuZ\nh8YkgiHUSiIfigqEypJC93iY3E3ZUFZUwNLJVUQNrN03tAjvtaOWhbHIVhLTakopLSrgyKmBtPUS\nB+yYxeSqEmrKrPfox+UUV4Dn093kVRJ+FYt3wfe7ruayHWu+1ocfIlkU+eVNlvf342Lz20Y+32uU\nsUuolUQ+MQmAmlJXSRSPgiUBxDZCen5P/N7b/ZEoW2031KIGyy1VWCCxZoKJwW6vv9Vpgz6zroya\nUstj2OljP21v2qzf/be7B7Kvx4jvEeVvwYlkcY0ji2geC7hvN1he7dWztTyyt1Qy+eGz/dQ/03qC\nG+7ZdEa2IdGYRDAEriRE5AsiEhWRes+5r4rIdhHZJiLXBvXsmjI35DIa7iaAS20lsW5fJ6c8C/Pm\nQ6foHogyp74sLn6yqMGyKloOJQ92A+yxC/Rm1pXF3qOfSm1vlXZXX8SXi8arJHJJm/Xb/mMwh8U4\n3voI3pLI1lrJ1rjJ9h34estZfuyd9iNhbUOijDyBKgkRmQ5cA+zxnFsM3AosBt4G3CUpIq75xCQA\nqku97qbRURINVSUsn1pFX8Tw+Bvur7OnW63d87ytPMDaqxvg5YTMGMff2jMQYV97LwViBbwnVlrB\nSKcoLx1ed5PBnzXR3Z99sNvbSDCIDrWOLPJREn5jJd65BO2FyVqpGJOVHz6I7Webd7XzxtHULfRH\nEo1JBEPQlsT3gb9NOHcz8IAxZtAYsxvYDlwcxMMdVwyMniUBcPM5EwF4qOUI3f0RjpzqZ03rSQS4\nbsH4uLHnTammuEDYfqyb9p6hC/9rR7qJGKsleXlxIRPtAP1RX1Xa/tqSezmdQyPBQZOnkvBrSURy\n/5Xv99MQySKgHnaGe/YHOvr45updfOa3rw/znZUwEZiSEJGbgH3GmJaEl6YB+zzHB+xzQ8g3JlFe\n7L690VQSl86sZeHECo53D/CNp3bxT0/vYiBquHL2OKbUlMaNLSsq4Pxp1RjgmVZ3r27H3+r0jXK6\n0k60XVV+LAnHcphgWx9+lERO7ibP4t3vO4vKHed3P4n+PNJz/VoS+cQ9so5gZHlB1Pjww+fZoDEd\n2bYRMcYEYs04aEwiGPKqkxCRJ4FJ3lNYH8uvA1/DcjXlzJo1a1i/fj2NjY0A1NbWsnTp0phZ6Xwo\nUh0f2Pr7LWwZAAAgAElEQVQynbvaqZm7nOICyTg+yOMvXtnIR7//IGtao9TMXc74imLON3tobj4w\nZPy1C5awdl8n9z7yJBNONnLFFVcA8Odnn+U3T++Gaedy+axxNDc3c/DoaaCBI6f60z4/agy7W9YR\nMXDhVVdw7PQAzzY30zmlOu38t2w9CgWzLHm++jLNk45nfL8zz70QgM7WTbzeVwOXzcgon97BKJ2t\n1o+CyBWNacc7vLbhRTpbT1IzdzlRY3z9e3S2bqdm7nIKxN/nwdo/pAGA55ubqS4rSjveWgStLsRb\n1r9IaVtNRnmBpfB3t6yjuWCv7/GvbXiJI9370463lG917LiwQNKO72rdTvXc5Wmf7xxvWvcCna0H\nqPEx3hjDbd95gALggS+/39f9/R5ffMlllBQV0NLSMiz3OxOPm5ubWbVqFQCNjY00NDTQ1NTEcCBB\naHYRORd4CujGUhzTsSyGi4GPARhj7rTHPgbcYYx5KfE+q1evNitWrMh5Hr9Yf5BfbToMwPdvnM+S\nSUO3Jh1J9nf08vCrRyksEN59bsOQgj+H/kiUDz3wKid6Bvm7t87iqjlWd9nm3e1886ldNFQVc99t\nSygQYe/JXj7xm21MrSnlP249J+WzT3YPcNuqLVSXFnLl7HH8/rXjfPrS6dy8ZGLaOf/zn/fy2BvH\nARhXVsSDH1ya8X3uOtHD//jv1wB4y9w6vvqWWRmveab1RCxYevvKGbx90YSM19y99gAPbrb6Hf3s\n3YuYae/JkY5r794IWPGcu9+zOOP453a3842ndgHwq/efy/jK9AVpkajhbfdYyu6LVzZybYI7Md2c\nrltQ76tI0xn/iYuncut5k9KO7RuMcuN/vALA7z+6LOOWr9f/fGPMYnriE+enHbv5UBdf/P0OX2MH\nIlHe/gtrHo9/fPmwtXl/cPNh7l57kP993RwunlGb+YKzhA0bNtDU1DQsQg7E3WSM2WKMmWyMmWOM\nmQ3sB843xhwBHgFuE5ESEZkNzAPWBjEP7/aWxQWjn+07vbaMz1w2g7++ZHpKBQHWTnh/eYHVMPCu\nF/Zz5FQ/XX2D3L32AADvWToplsI5scoOXJ/qT+vLP2b3EZpQURzrM+Wn2+xJT1wkyH0regezj0l4\nq8F7fNZ9OPj1Pmab3ZSXeyqA8SbF38NBNvPNphV8JGr4zpo9/PH14xnve/fagwD8zP6/MvyM1MoZ\nazVkjNkKPAhsBf4AfMqkMGfyjUl4d6MbhVq6vLh+wXiWT63iZM8gf/WbbdzyrVUc7Oxn7vhybljk\n/jotLy5kQmUxA1GTtOeTg9NsbnxlMZOrrDiIny08TyQoCT8LeC5KwjsuUzGXY2Z7Yx89WXRdhWzq\nJDx/+1IS2Y33kn0KbJa9m0Yx7h5flJh+Ii8f6OSp7Sf4/rN7/T/AT3xGyYkRWTpti+KE5/hbxph5\nxpjFxpgngnpuSWG4LIlsKCwQvv7W2Vw4vZrugShdfRHmjS/nG9fMiXtf4PZ+2tueetF3dsCbUFES\n6zbb5sOSSOxk6s12SkUuVdq59JXyKhO/FeQOuVgSfiyDSB5puUGs4XHbwvoYH1R6R3x1fPqx3Tns\nBnhm552Fm1A3+Mu3TsLrbhqtOol8qCkr4p+um8v+jj76BhcyZ3x50l/AjePK2HCgi73tvbHivUT2\nd1gFeFNqSmLdZg929hE1JuWv6kjU0N5jZUA1VBVz5NQAnX2DcUWKychlwe/N4honcBfvbvLXLt3B\nryWRTU+poeOzmlLW/qaoya42wE/8UUSGPw2KBDdcBsHkuhtgOlkMRg33b2zjTTNqYh0OUpHuO3E2\ncmb9vM4Sb+fX0UyBzQcRYca4MuZNqEj5wXUsiX1p9tN29q2YUVsW2xCpZyD9hkhtXf1EjZUyW2d3\nEE2stUhG/ILv7wvvtVD6fVZpe9Nm/TQ4zCVJw2sVRX3ou4EslYqXYJt++COob0k2bVeC2Ev9D68d\n4/6NbXz2kTfSjjvZPcAt923m31/cn/0kxiihVhL5xiS8SmK0ejcNF+n8rTPrLCWRrHusg2NJTKu1\nrIh5461MoB3HU1fLOtfMqC2LVa/7aSTotQT89oiK2441gyXhyCJupz0floRX+Qz6WfHJfo/vwTw2\nacql4jobP/xwt/HIZrrxsRr/Y7MhnSwOd/mr6XjsjeN0D0T5zZajuU1iDBJqJZEv3jhE4RmuJNIx\nb3w5BWKlniZz1fQMRGjr6qdQrE6zYO1FAbAjxa554FomM8aVZtVI0LvId/QO+vpF7bVQcnFR+Qlc\nx+/Ml0NPKV/uJm9RoK9HxAjCOxWWIvFs3E25kOmOo/X1f+CVNn720oHRefgwEWolkW9MwhuHGM5N\nh0aDdP7W8uJCZtWVETHJF/0dx3uIGphdXx7b63ux7Zfd3Ja6kaB3UyQnDtHZm527KWriGwumwmtJ\n+I1JeIPV3T4C6t7xvYP+YhhxwXEfiqg/j1Yh2eItjPNDkNXOmcimrXsQMYnRijHcs+4Qv2454qu7\nQVgJtZLIl5KCMz8m4ZeFE61Ff1uSZmuv2+fmT6iInTtvchWFYr12KoV18Krdyvychsqs3E2Ji6kf\n6+OYp61ILpZEu695ea0VfwtRvEsrO2sl+zqJ7Oow/Hyks62TCCwmkUWWWG4xifSvF/j8/mejS7JZ\n+PPtUtzSdoont2euGwmCUCuJfGMSRWMgcO2QyffsZGxsTbJVamzfiomukqgoKeScSdaGSC/uHboh\n0pFT/Rzq6qe8uIDZ9eWMr7AC1yeSNB1MJPFX/cme9F+mSNTEpdpmSpt1ZOFdkE90Z/7Cegvu/MQw\nEp/hy6XleUYQKbBxgfQsawP8LL6BpcB6RJfZksgeQ3pZDPf7enL7cd77ny3cv7FtmO+cnC88up3v\nrtnL3jTJKUERaiWRL97S/+FqAxBWlk2xWo5sOtg1JFd/00Gr7fjyqdVx17xlrtXu44kkv1Cad1ub\nJF04vYbCAok1BTyWRSNBh3RFfgDtPYNxvy79WhLeRf+kD+XltWgixt8ObL15WBJ+mxvG8LE6eu8Z\nSB1GFt+TbJ4eySYFNqcf3ekv8m1J+FQnv1h3CIB7Xz7ka3w6DnT08cfXj/uKeSXrDB00oVYS+cYk\nxpJayOR7nlpTyrSaUk71R9h2xLUmXjt6mlP9EabWlA7pOPvmOeMoKRQ2HTxFqyfLKWoMj247BsBV\ns8cBVhEe+FMSTjrrDDuT6kBHeiVxyFYijrWXaTF2ZOHtUHuiO/O8Et0DfqyJ+DhG5kW/J4euuQ7Z\nWhKRAPaTCCpuEbcfeSZ3U47PSCeL4Q5JlhVnXjq9skx8T0dO9fN3j7Wy+VAXH/31Vr7/7F6e2u5/\nN8A/vnaMP7x2zPf4fAi1ksiXM9zDlDUXz6gBrKZ0Dn+y242/qbFmyPiq0iLevthqpPevL+yP/bJ+\n/I0T7O/oo6GqmMtm2UoitrmR/30rFtousIMZ2n/stnfac3blO+0nnXUwykDEUChQWih09kVSxlYc\nOhLcXn7iEvEZUdlZEn4tIgc/i6PXkvCTJRS3UGVZMZ4J7/MzKZes2pvkoKgyXeLXQPK7ZHi7Hqzd\n15G0mNMrykT5/Pi5fazb3xlrkAjQejx1CrsXYwzfb97HD5r3BbYjo5dQK4l8YxLVpaEuKM8KP75n\nx3301I6T9Eei9AxEYjvgXTOvPuk1H1g+mXFlRWxpO803ntzJ/Rvb+Nfnre0+PnLB1Niv++rSQkoK\nhe6BaMZMImcHPCcG4my3mopddhbVuXaX3kzZUM3NzXTZz6guLWK6U0yYwWJJtCT8KKNslUR3Dps0\nOfhZG+OzpzJ/LrINXPusY7TH+g9Gx1kSGQZn35Qjc0yi0KeWOOCjnxnExzi//vhOvvOnodu9pmv2\nmE+2Uz79wXIh1EoiXxqqSvjSVTP59g3zRnsqI8LCiRXMriujo3eQx14/zm+2HKWrL8Lihgrmjk/e\nRrumrIhvXDuHiuICXtrXyb0vH6I/Yrhx8QSa5tXFxon4j0s4i/yyKVYG1Z723rQ9n7bYabgXTKtG\nsKqnMy0kp+1nVJUW+qo4BziRYEn4ydSK25nPh1Lp6POOz3a5y/yFz7a4L7u7u/hZUr0xnUz3zqaY\nLpDsJh9Koj8S9dV5FoY2DH1uT8eQMdmk/QK+hG5Mctfd8dMDfPI323zPPxtCrSTyjUkAXD2/nvMT\nArZnIn58zyLCB1dYLcb/5fn93GcH1T5ywdS0gfvFDZX82y2LuO28Bq5bUM8/NM3mM5dNH3LNJKd7\nbIZAtBO4rq8oZt6ECqIGXj2cvB7jZPcAu072UlIoLJ5USWWJlWqbTqmsXLmSrn7rGVUlhcy0lcT2\nY+nNdcft5exY6Cdttt2jWPy0I/e6tPw2N3Tws4545RKNZo5JmGxNCRs/rtrBuEyr9DePZGFJ5Er6\nOonM12fTbt6PZRJfQBj/WrLL/ShmQ4LCtQ/u39TGnpO92XXO9UmolYSSPStn1fIOz4Y9H7pgCudP\ny6wkJ1eX8vGLp/GFK2eycva4pErFaemRziSPRA3dA1EEqCwp5KLpVixkzc72pOOf2Wm5w1ZMq6ak\nsIAqux7jVAaXlrNYVpUWcq69lWtLW1faa5wA+jl2rMSPye8dkymVF6C9N/t6j9h4H0qlw1PMmG3y\nVDQLLeFts5+KOEsik7spi8aHQbhQhruYzk8Hh3RuoWRZVH5nGG9J2H8H6HUKtZLINyYxlvCbDy8i\nfHblDP79lkXc897FfPD8ycM2B6elR7psJWdRrSkrokCEt9ouq2d3tQ9J3+uPRPnvLdbOctfMt/bI\nqLItiXRxiebm5thzqkuLWDSxkpJCYeeJXo6kaH9+snuA9t5ByooKYq63TO6m3sFoQi1G5gyqNk+P\noGzdTX5aZMen8WbXuymbtbe8uDDjmGxalkTSLJiJeF/2m21lSC8LX4WHWQjIz/3iYxLZreJtXX1s\nT9EyJ86NZR8E2XYo1EpCyZ3Z9eVMry0b1nv6sSRimxtVWEkD02vLuHB6Nb2DUX760oHYF9EYw8/X\nHuTIqQFm1pVxmd3i3LEkMjUGdH7V15cXUVJUEGuR/mSKNMItTkFhQ0WsMPDoqfSLfmI2VKZaDGNM\n3EZO2bqbun3EPLzWTLZuGz91IQ7lPlI8I9lYElm4m3Jpt545uynzIprNOp69JZH5nt45fui/tvLp\nh19Pmk0YSSIfH4ZfzoRaSQxHTGKskE0+fFD4sSQcJVFf4e4F/VdvmkZpofDUjpP8wxM7eWTrUe54\ncif/79WjFAr8f5fPiH3pqkos5ZIpJnHSfk6d/Zzr7L2kH371aNJrn99jubuWT6n2KLv0gW4n9jLb\n7rJ7vHsg7S/Co6cH6PPulpetJeFDSbR5lJCfOgnvbDNZNt735kdJeK2szIFrd0SmVvDxrU38WhL5\n10lko3P9uK+iaSwtv96vN5K02Um2pW5RgFtvhlpJKOFicnUJhWIVAqVK73QtCVdJzKor5++aZscy\nqP7l+f28uLeT0qICvvbW2SyZXBUb6/SI6soQk3AylerKLaVywbRqzp1cSUfvIN9ZsycuC+hARx9r\ndrYjwFVz6phWYy36+zOkzDrZUgsmVlBfXkR/xKRtOe30ulo+1Xo/nT474DokWi7J8LZlyDb+25Oh\nqaG3E6+fymOvEszobvJ8XE71Z3DzeZSl7/eYZtypvkFfabXZZIv5CVz3xmWixb+W7Opk53oGokOK\n8uID19b/g2w7FGoloTEJlzDs31tcWMCMcWUYYHeKvStOJFESAJc01vLTdy/mwxdM4foF4/nohVP4\nj1vP4Qq7otuh0mdMwnH9OJshiQhfuKKRqpJCXtjTwe2PvMHv7arUrz62g8GooWleHdNqS5lcXUJR\ngXD09EDamg9vF1yntXq6gqe1+6w0yBXTqqksKSRi/HXAdeIwfRETp9wS6R2MssPz/Eg0c0zCu8Bk\nsmy8rjI/ys1rsWUaPuBJ7zmeoc+WdwOpdPLwkmq/747eQW75ZQs/bN435LXEArh0SuK1I6d5wxMj\n8PPD/bgnVXxIvCNZdlOSc/2RaHw8J2qSBq7PWCUhIn8jIttEpEVE7vSc/6qIbLdfuzbIOSjDixP0\nbU2hJJJZEg4NVSV84PzJfP7KRt6/fHLSMbV2S/JMmUduTMK9x7TaMr71trlMqCxmx/EefmhXpbZ1\n9TNvfDmfvmwGYPmT50+w3keqVunGGDbaPa/OnVwVa62+bv/QZohgbWrz512WS+uq2XW+3wfEt7FP\n18CteVd7nL8+25hEJiWx62R2Voo3RpNJqfR7qtt/+tIBfr35cMqx3oSCW37Zwrp9yWXuKGWA0/Z7\ni5r4RTRZw0tjDL9Yf5Cb790c18Im1T5Ukajhs4+8wWcefj0mfz/upn/2pKMmytNvj6i+wWicMoua\nhGaJ9o2D3FQtMCUhIm8GbgSWGmOWAt+zzy8GbgUWA28D7pIUUSWNSbiEISYBMKfeWlx3pvhF7RTa\nja8cqgD84LiP0jUyu/zyy2NZTBMSnrNwYiU/f89iPnv5DN4yt46r5ozjs5fP4Ac3LohZKQAXTLNS\nc5/dlTw19+UDXRzs7KeuvIgFEypYabcnWbPzZNwvRLBalXxz9U4GIoY3zxnHlJpSxtlKwk8thnd9\nddqoJHLkVD/3rD8IwKWNVpA+25hEujgPwNq97qLrx5I41u39pZx+7EDCCvyztQfjjp1f2r2DUV4+\nEJ/K/MPnkuf+f/3xnbG/+wajrFy5ki/9fgeffvj12PyTrZ2n+iP8apOlpH65wW3Ql8qS8KYyO//2\nfvanKfNEk/20UEl2x/6IGeLWi9/YKvjspiD7Vvw1cKcxZhDAGON0o7oZeMA+v1tEtgMXAy8FOBdl\nmJibwe3iFKxNqS5N+nomxtlKIl1NQkfvID0DUSpLCmMxDC/lxYW8Y/EE3rF4QpKrLZrm1bNqUxur\nd5zgspm1XDazFhGhPxJl3b7OmHviXedOpLBAmF1fzsUzali7r5PPPvI6V8weR3FhAXtP9rJ+fycD\nUcPk6hL++tLpgKskU6XkevEuH79uOULEWHGNksICTvYMsvXwKZ7cfoLugSjnNFRy/cLxvLC3w1+d\nhOfm6ayUjQe6eCFOSWS4rTHsPuGxPDJMYyBNsPpHz+1j08EufvKuRXz+d28MqZFx/P/r93fy6LZj\nfP6KxtgmWF4iUROzDDt6B6krL07qwvFmtXnTjlNZZt4sNWeB9lNHsmRSVcw96CcmkWyy/ZFoXIZT\n1MDpuDlb/y/xKK3hLlYMUkksAK4Ukf8D9ABfNMa8DEwDXvCMO2CfG8KmTZtYsWJFgFM8c2hubg6F\nNTF3vNWPqfVED5GoifsFE4m6KaCJHWf94sQY0imJ3z+1BhjPlOqSnFvAT6st5ZZzG3io5QjfeGoX\nlSWFlBUV0NE7GHMprJhWzXuWTopd84UrGvn6E61sP9bDf3v2QBZg5axx/M1l02Pzd1qFZOpbBe6v\n6JvPmchvtx7loZYjPNRyZMi4N82o4UtvnhnbRMqpk/D7uXh6xwkuml7D5JoSolFDe88gezv6WL+/\nk+d2txM1lpXywt6OjJZES9vpOCspU41BskSHHz23jxsXT4h1HN586FRczMXB+Yx97bFWAGrLDvK5\nKxqHjFu95s+AZSF29UYsJZFkOd7qcTE5xY8DkWisPb73PYlInKtswP5sZMrQgvhNrhLlWZTEEqlI\nklF2vHuA1464sZCIMXEFm8mym/w04cyGvJSEiDwJTPKewvrt8nX73nXGmEtE5CLg18CcbO6/Zs0a\n1q9fT2Oj9YGora1l6dKlsS+FE6jS45E9nlZTz4HOPh78w2pmjCuLvf7ok3/i5I7dzFl6EWVFBTnd\nv6N3ABhHe89AyvEneqwvwcDeFpqbj+X8fhb17eSK4nZeLZ7Fie5BDm17GYBlF17CdQvHU3/iNV58\nvi02/tUNL3FbvaHiwmVsP9bN6xvXUldexPvfcTUNVSVx959VV0Zn6ybWdFTwsYtuSzsfYy9s83pb\n+fCkAdrHL2JfRy/7tqynvLiAlStXctmscRx5bQOvrDtEzdxlAOzZso6Wqva079fy71vuqd1b1vPX\nW9ZTM9dy43a2WokhNXOXUyBwgdnDsmgNL1AXFwj23q9vMEpk6hLuWXcw7nrvBkjJ5nO6PxI3HmDV\no0+x6lH3+Bv/8Qid3QND5ld4wSVxx/smXz5k/gAP/2ktnf0TqJm7nO3Hu9m9ZZ2tUBvixv/cdjt2\ntm6iE3hnzyB9g1FO7oi/37PPNlNQIExceH5s/NoXjjPrhqvpH4wOef73f/UHCgSWXHAJUWP49R+f\n9sgnXp5Tq0v5U+uzcdfvf/Vlmk/VxuTX2bqJB1qJk8crtW2UNJ4XO17/4nHmv+NqXn35RXb+1y8B\n+MALjXzg8kU0NTUxHEhQ/eNF5A/At40xa+zj7cAlwCcBjDF32ucfA+4wxgxxN61evdqoJRE+/u+f\n9/D4Gyf4n5dM45ZzG2Ln1+/v5GuPtbJ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "@interact \n", "def space_cut_frequency(n=(0, mat.shape[1] - 1)):\n", " \"Plots time profile at fixed position.\"\n", " sig = mat[:, n]\n", " X = np.fft.rfft(sig)\n", " freqs = np.fft.rfftfreq(sig.size, d=dt)\n", " plt.plot(freqs, 20 * np.log10(np.abs(X)))\n", " plt.xlabel('frequency (Hz)')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can superimpose a few cuts on the same graph:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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EyB4bZHjIzYP37mLLvbtobRoiNy+L+ta3AOibp1kg44WFZPk9hLJzOPGnHXHn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\nbaKVhEaj0WjaRCsJjUaj0bTJ/we1QSkLQEY3agAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "space_cut_frequency(1)\n", "space_cut_frequency(25)\n", "space_cut_frequency(49)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "An interesting conclusion from this Fourier analysis is that each individual time signal is composed of a number of discrete harmonics. This is an expected result, as a vibrating string only allows frequencies that are multiples of a frequency \n", "\n", "$$\n", "f = \\frac{v}{2L} \n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In our case, this frequency should be:" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "50.0" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "100 / (2 * 1)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(0, 300)" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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Vyy1nFcZ8fw8/2d3QycqKGsp2Oaul5qcl8pVLS6K6D8bexk6+/Ocq2nsCfGDh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\ny4FvANcZY/pEZIIx5qiIzAd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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "space_cut_frequency(49)\n", "plt.xlim(0, 300)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "By looking at the above plot, we can see that the fundamental frequency is indeed 50 Hz, but that the following frequencies all seem to be odd multiples of the fundamental frequency. I believe this is a consequence of the fixed conditions that are imposed at the boundaries of the string and that \"force\" even multiples of the fundamental to be zero. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Conclusions " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this notebook, we have used a simple 1 dimensional finite difference simulation of the wave equation. This has allowed us to do several things: animating the solution, examining its variations in space and also frequency domain. In particular, it is interesting to see that even multiples of the fundamental vibrating frequency of the string were not observed." ] } ], "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": "3.5.1" } }, "nbformat": 4, "nbformat_minor": 0 }