{ "metadata": { "name": "", "signature": "sha256:95e466d7c100f004e20c6099e2cf48372e8a3fe93aae4ab78645e33d34b76ab2" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "An incident wave \n", "\n", "$$ u_I(x, t) = F_I(t - x/c) $$\n", "\n", "arrives perpendicularly at a boundary separating two media gives rise to a reflected wave \n", "\n", "$$ u_R(x, t) = F_R(t + x/c) $$\n", "\n", "Writing that the disturbance is zero at the boundary (which we set on the origin) we obtain the following \n", "\n", "$$ u_I(0, t) + u_R(0, t) = 0 \\; \\forall t \\Rightarrow F_R(t) = - F_I(t)$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the following lines, we plot that relation with a given waveform." ] }, { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib inline" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "code", "collapsed": false, "input": [ "from pylab import *" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "code", "collapsed": false, "input": [ "t = linspace(-10, 10, num=1000)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "cell_type": "code", "collapsed": false, "input": [ "def waveform(t): \n", " return sin(5*t) * exp(-abs(t**3))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 4 }, { "cell_type": "code", "collapsed": false, "input": [ "plot(t, waveform(t))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 5, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "By plotting the waveform at different $t - x/c$ (with $c$, the speed of the wave implicitly equal to 1) values, we can see it move forward." ] }, { "cell_type": "code", "collapsed": false, "input": [ "x = linspace(-10, 10, num=1000)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 6 }, { "cell_type": "code", "collapsed": false, "input": [ "plot(t, waveform(x), label='t=0')\n", "plot(t, waveform(3 - x), label='t=3')\n", "plot(t, waveform(7 - x), label='t=7')\n", "legend(loc='lower left')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 7, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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YVz4P88rj+FZSaWgA/vu/E7cTGumny94BgF//Gnj9deCqq7g0TgVCok9kNcEy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\nRJvNhpdeegl1dXXQ6XTYt28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"text": [ "" ] } ], "prompt_number": 7 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Writing a function that sums up the adding of the waves gives the following result." ] }, { "cell_type": "code", "collapsed": false, "input": [ "def plot_timestep(x, t):\n", " # incident wave\n", " inc = waveform(t - x)\n", " plot(x, inc, label='incident')\n", " # reflected wave\n", " ref = - waveform(t + x)\n", " plot(x, ref, label='reflected')\n", " # sum\n", " plot(x, inc + ref, label='sum', lw=2)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 8 }, { "cell_type": "code", "collapsed": false, "input": [ "figure(figsize=(10, 7))\n", "for ind, val in enumerate([-3, -0.5, 1, 4]):\n", " subplot(2, 2, ind + 1)\n", " plot_timestep(t, val)\n", " grid(True)\n", " legend(loc='lower right')\n", " title('time = %i' % val)\n", "tight_layout()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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a8toQFgtHW65A9rLCAnkkMYJVmmVP5EEGuAc5YhdvFymCrEtDnm9VwF7tAhDW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MF7zQWyrUYSyJYmSSCP7DOmQCYIQhtKOFgKD7KWEAtxcEBaKJc8x0JTk7ROvVL6gLFRgZzoN9cq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\nqwDIAduXXXYZAKCtrQ3z58/H7Nmzce655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"text": [ "" ] } ], "prompt_number": 9 }, { "cell_type": "markdown", "metadata": {}, "source": [ "This can now be compiled into an animation, courtesy of [this nice article by Jake Vanderplas](http://jakevdp.github.io/blog/2013/05/12/embedding-matplotlib-animations/) and [a helpful comment](http://jakevdp.github.io/blog/2013/05/12/embedding-matplotlib-animations/#comment-944929859)." ] }, { "cell_type": "code", "collapsed": false, "input": [ "from tempfile import NamedTemporaryFile\n", "\n", "VIDEO_TAG = \"\"\"\"\"\"\n", "\n", "def anim_to_html(anim):\n", " if not hasattr(anim, '_encoded_video'):\n", " f = NamedTemporaryFile(suffix='.mp4', delete=False)\n", " anim.save(f.name, fps=20, extra_args=['-vcodec', 'libx264', '-pix_fmt', 'yuv420p'])\n", " video = open(f.name, \"rb\").read()\n", " f.close()\n", " anim._encoded_video = video.encode(\"base64\")\n", " \n", " return VIDEO_TAG.format(anim._encoded_video)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 10 }, { "cell_type": "code", "collapsed": false, "input": [ "from IPython.display import HTML\n", "\n", "def display_animation(anim):\n", " plt.close(anim._fig)\n", " return HTML(anim_to_html(anim))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 11 }, { "cell_type": "code", "collapsed": false, "input": [ "from matplotlib import animation\n", "\n", "# First set up the figure, the axis, and the plot element we want to animate\n", "fig = plt.figure()\n", "ax = plt.axes(xlim=(-10, 10), ylim=(-1, 4))\n", "line_inc, = ax.plot([], [], lw=1, label='incident')\n", "line_ref, = ax.plot([], [], lw=1, label='reflected')\n", "line_sum, = ax.plot([], [], lw=2, label='sum')\n", "vlines(0, -1, 4, linestyles='dashed', lw=4)\n", "annotate(\"totally reflecting wall\",\n", " xy=(0, 2), xycoords='data',\n", " xytext=(5, 3.25), textcoords='data',\n", " size=10, va=\"top\", ha=\"center\",\n", " arrowprops=dict(arrowstyle=\"simple\",\n", " connectionstyle=\"arc3,rad=-0.2\"), \n", " )\n", "legend(loc='center right')\n", "\n", "# initialization function: plot the background of each frame\n", "def init():\n", " line_inc.set_data([], [])\n", " line_ref.set_data([], [])\n", " line_sum.set_data([], [])\n", " return line_inc, line_ref\n", "\n", "# animation function. This is called sequentially\n", "def animate(i):\n", " x = linspace(-10, 10, 1000)\n", " t = linspace(-7, 7, num=100)[i]\n", " # incident wave\n", " inc = waveform(t - x)\n", " # reflected wave\n", " ref = - waveform(t + x)\n", " # sum\n", " total_wave = inc + ref\n", " line_inc.set_data(x, inc)\n", " line_ref.set_data(x, ref)\n", " line_sum.set_data(x, total_wave + 2)\n", " return line_inc, line_ref\n", "\n", "# call the animator. blit=True means only re-draw the parts that have changed.\n", "anim = animation.FuncAnimation(fig, animate, init_func=init,\n", " frames=100, interval=20, blit=True)\n", "\n", "# call our new function to display the animation\n", "display_animation(anim)" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "" ], "metadata": {}, "output_type": "pyout", "prompt_number": 12, "text": [ "" ] } ], "prompt_number": 12 } ], "metadata": {} } ] }