CompMech05-BVPs_project.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Computational Mechanics Boundary Values - Project 05\n",
    "\n",
    "![6-string guitar diagram](../images/guitar.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams.update({'font.size': 22})\n",
    "plt.rcParams['lines.linewidth'] = 3\n",
    "from scipy import linalg\n",
    "from IPython.display import HTML\n",
    "from IPython.display import Audio"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this final project, we will consider all six strings of a guitar and the deflection of the neck of the guitar. Here are the inputs for each of the strings, all L=0.64 m:\n",
    "\n",
    "|string|density (g/m)|tension (kg)|\n",
    "|---|---|---|\n",
    "|E|0.401|7.28|\n",
    "|B|0.708|7.22|\n",
    "|G|1.140|7.32|\n",
    "|D|2.333|8.41|\n",
    "|A|4.466|9.03|\n",
    "|E|6.790|7.71|"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. The neck of the guitar can be considered a cantilever beam with an applied moment, shown above. At the tip we have a moment equal to the sum of the (tensions in the strings) $\\times$ (bridge height). Here we will consider it as $h=4~mm$. \n",
    "\n",
    "a. Use a finite difference approximation to determine the deflection of the guitar's bridge if the Young's modulus is E=10 GPa and it is a rectangular cross-section $2\\times4~cm^2$ and $I=\\frac{4\\cdot2^3}{12}~cm^4.$\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Given \n",
    "E = 10e9 #N/m^2 \n",
    "A = .02*.04 #m^2\n",
    "I = (.04*.02**3)/12 #m^4\n",
    "h = .004 #m\n",
    "L = 0.64 #m \n",
    "\n",
    "Te = 7.28*9.81 #N\n",
    "Tb = 7.22*9.81 #N\n",
    "Tg = 7.32*9.81 #N\n",
    "Td = 8.41*9.81 #N\n",
    "Ta = 9.03*9.81 #N\n",
    "TE = 7.71*9.81 #N\n",
    "\n",
    "T = Te + Tb + Tg + Td + Ta + TE\n",
    "M = T*h\n",
    "\n",
    "#Solved Constants\n",
    "A = 0 \n",
    "B = M/E/I\n",
    "C = 0\n",
    "D = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 1000\n",
    "x = np.linspace(0, L, N)\n",
    "y = lambda x: M*x**2/(2*E*I)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finite Difference With 6 Segments A:\n",
      " [[ 7. -4.  1.  0.  0.  0.]\n",
      " [-4.  6. -4.  1.  0.  0.]\n",
      " [ 1. -4.  6. -4.  1.  0.]\n",
      " [ 0.  1. -4.  6. -4.  1.]\n",
      " [ 0.  0.  1. -4.  5. -2.]\n",
      " [ 0.  0.  0.  1. -2.  1.]]\n",
      "\n",
      "Deflection of the Guitar's Bridge: 1.4155 mm\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#6 Segments \n",
    "N = 6 \n",
    "dx = L/N\n",
    "\n",
    "A = np.diag(np.ones(N)*6)\\\n",
    "+np.diag(np.ones(N-1)*-4,-1)\\\n",
    "+np.diag(np.ones(N-1)*-4,1)\\\n",
    "+np.diag(np.ones(N-2),-2)\\\n",
    "+np.diag(np.ones(N-2),2) \n",
    "\n",
    "A[0,0] += 1\n",
    "A[N-2,N-1] += 2\n",
    "A[N-1,N-2] += 2\n",
    "A[N-2,N-2] -= 1\n",
    "A[N-1,N-1] -= 5\n",
    "\n",
    "b = np.zeros(N)\n",
    "b[N-2] += -M*dx**2/E/I\n",
    "b[N-1] += M*dx**2/E/I\n",
    "\n",
    "w = np.linalg.solve(A,b)\n",
    "x_num = np.linspace(0, L, N+1)\n",
    "\n",
    "print('Finite Difference With 6 Segments A:\\n', A)\n",
    "print()\n",
    "print(\"Deflection of the Guitar's Bridge:\", round(w[-1]*1000, 5), \"mm\")\n",
    "\n",
    "#Plot/Labels\n",
    "plt.plot(x, y(x), label = \"Analytical\")\n",
    "plt.plot(x_num, np.block([0,w]), 'o' , label = \"Numerical\")\n",
    "plt.xlabel(\"Beam Location (M)\")\n",
    "plt.ylabel(\"Defelction (m)\")\n",
    "plt.title(\"Finite Approximation\")\n",
    "plt.legend(bbox_to_anchor = (1,0.5), loc='center left');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "b. Demonstrate that your finite difference solution has converged. _e.g. decrease the step size $h$ and show the solution converges to a final value._"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Deflection of the Guitar's Bridge: 1.4155 mm\n"
     ]
    },
    {
     "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": [
    "#20 Segments \n",
    "N = 20 \n",
    "dx = L/N\n",
    "\n",
    "A = np.diag(np.ones(N)*6)\\\n",
    "+np.diag(np.ones(N-1)*-4,-1)\\\n",
    "+np.diag(np.ones(N-1)*-4,1)\\\n",
    "+np.diag(np.ones(N-2),-2)\\\n",
    "+np.diag(np.ones(N-2),2) \n",
    "\n",
    "A[0,0] += 1\n",
    "A[N-2,N-1] += 2\n",
    "A[N-1,N-2] += 2\n",
    "A[N-2,N-2] -= 1\n",
    "A[N-1,N-1] -= 5\n",
    "\n",
    "b = np.zeros(N)\n",
    "b[N-2] += -M*dx**2/E/I\n",
    "b[N-1] += M*dx**2/E/I\n",
    "\n",
    "w = np.linalg.solve(A,b)\n",
    "x_num = np.linspace(0, L, N+1)\n",
    "\n",
    "print(\"Deflection of the Guitar's Bridge:\", round(w[-1]*1000, 5), \"mm\")\n",
    "\n",
    "#Plot/Labels\n",
    "plt.plot(x, y(x), label = \"Analytical\")\n",
    "plt.plot(x_num, np.block([0,w]), 'o' , label = \"Numerical\")\n",
    "plt.xlabel(\"Beam Location (M)\")\n",
    "plt.ylabel(\"Defelction (m)\")\n",
    "plt.title(\"Finite Approximation\")\n",
    "plt.legend(bbox_to_anchor = (1,0.5), loc='center left');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Deflection of the Guitar's Bridge: 1.4155 mm\n"
     ]
    },
    {
     "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": [
    "#50 Segments \n",
    "N = 50 \n",
    "dx = L/N\n",
    "\n",
    "A = np.diag(np.ones(N)*6)\\\n",
    "+np.diag(np.ones(N-1)*-4,-1)\\\n",
    "+np.diag(np.ones(N-1)*-4,1)\\\n",
    "+np.diag(np.ones(N-2),-2)\\\n",
    "+np.diag(np.ones(N-2),2) \n",
    "\n",
    "A[0,0] += 1\n",
    "A[N-2,N-1] += 2\n",
    "A[N-1,N-2] += 2\n",
    "A[N-2,N-2] -= 1\n",
    "A[N-1,N-1] -= 5\n",
    "\n",
    "b = np.zeros(N)\n",
    "b[N-2] += -M*dx**2/E/I\n",
    "b[N-1] += M*dx**2/E/I\n",
    "\n",
    "w = np.linalg.solve(A,b)\n",
    "x_num = np.linspace(0, L, N+1)\n",
    "\n",
    "print(\"Deflection of the Guitar's Bridge:\", round(w[-1]*1000, 5), \"mm\")\n",
    "\n",
    "#Plot/Labels\n",
    "plt.plot(x, y(x), label = \"Analytical\")\n",
    "plt.plot(x_num, np.block([0,w]), 'o' , label = \"Numerical\")\n",
    "plt.xlabel(\"Beam Location (M)\")\n",
    "plt.ylabel(\"Defelction (m)\")\n",
    "plt.title(\"Finite Approximation\")\n",
    "plt.legend(bbox_to_anchor = (1,0.5), loc='center left');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " __Discussion:__ From the graphs above, we can see that as we increase the number of segments for the finite approximation, the solutions better represent the analytical solutions and they show that it fully converges. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2. Here we will record the first three frequencies of the 6-string guitar. \n",
    "\n",
    "a. Consider the G-string on the guitar, L=0.64 m, $\\mu=1.14~g/m,$ and T=71.81 N [1]. \n",
    "\n",
    "__Guitar string equation:__ $\\mu\\frac{\\partial^2 y}{\\partial t^2}=T\\frac{\\partial ^2 y}{\\partial x^2}$\n",
    "\n",
    "a. Calculate the first, second, and third natural frequencies using 6, 30, 45, and 60 nodes. Plot the mode shapes and determine the number of nodes needed to converge for the first three modes. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Given \n",
    "L = 0.64 #m\n",
    "mu = 1.14e-3 #kg/m\n",
    "T = 71.81 #N"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The First 3 Natural Frequencies of a 6-Element String (Hz):\n",
      "1st Frequency: 194.4371 Hz\n",
      "2nd Frequency: 379.1243 Hz\n",
      "3rd Frequency: 544.8006 Hz\n",
      "\n",
      "Longest time period = 5.143 ms\n",
      "shortest time period = 1.174 ms\n"
     ]
    },
    {
     "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": [
    "#6 Nodes\n",
    "N = 6\n",
    "dx = L/(N+1)\n",
    "k = T/dx**2/mu\n",
    "\n",
    "A = k*(np.diag(np.ones(N)*2)\\\n",
    "       -np.diag(np.ones(N-1),-1)\\\n",
    "       -np.diag(np.ones(N-1),1))\n",
    "\n",
    "e,v = linalg.eig(A)\n",
    "isort = np.argsort(e.real)\n",
    "\n",
    "e = e[isort]\n",
    "v = v[:,isort]\n",
    "\n",
    "first = e.real[0]**0.5/2/np.pi\n",
    "second = e.real[1]**0.5/2/np.pi\n",
    "third = e.real[2]**0.5/2/np.pi\n",
    "\n",
    "print(\"The First 3 Natural Frequencies of a 6-Element String (Hz):\")\n",
    "print(\"1st Frequency: {0:.4f}\".format(first), \"Hz\")\n",
    "print(\"2nd Frequency: {0:.4f}\".format(second), \"Hz\")\n",
    "print(\"3rd Frequency: {0:.4f}\".format(third), \"Hz\")\n",
    "\n",
    "f1 = np.sqrt(e.real[0])/2/np.pi\n",
    "fn = np.sqrt(e.real[-1])/2/np.pi\n",
    "print('\\nLongest time period = {:1.3f} ms\\nshortest time period = {:1.3f} ms'.format(1/f1*1000,1/fn*1000))\n",
    "\n",
    "#Plot/Labels\n",
    "x = np.linspace(0, L, N)\n",
    "\n",
    "plt.plot(x*10, v[:,0], label = \"First Mode\")\n",
    "plt.plot(x*10, v[:,1], label = \"Second Mode\")\n",
    "plt.plot(x*10, v[:,2], label = \"Third Mode\")\n",
    "plt.xlabel(\"Nodes\")\n",
    "plt.ylabel(\"Displacement (m)\")\n",
    "plt.title(\"6 Nodes\")\n",
    "plt.legend(bbox_to_anchor = (1,0.5), loc='center left');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The First 3 Natural Frequencies of a 30-Element String (Hz):\n",
      "1st Frequency: 195.9946 Hz\n",
      "2nd Frequency: 391.4862 Hz\n",
      "3rd Frequency: 585.9728 Hz\n",
      "\n",
      "Longest time period = 5.102 ms\n",
      "shortest time period = 0.259 ms\n"
     ]
    },
    {
     "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": [
    "#30 Nodes\n",
    "N = 30\n",
    "dx = L/(N+1)\n",
    "k = T/dx**2/mu\n",
    "\n",
    "A = k*(np.diag(np.ones(N)*2)\\\n",
    "       -np.diag(np.ones(N-1),-1)\\\n",
    "       -np.diag(np.ones(N-1),1))\n",
    "\n",
    "e,v = linalg.eig(A)\n",
    "isort = np.argsort(e.real)\n",
    "\n",
    "e = e[isort]\n",
    "v = v[:,isort]\n",
    "\n",
    "first = e.real[0]**0.5/2/np.pi\n",
    "second = e.real[1]**0.5/2/np.pi\n",
    "third = e.real[2]**0.5/2/np.pi\n",
    "\n",
    "print(\"The First 3 Natural Frequencies of a 30-Element String (Hz):\")\n",
    "print(\"1st Frequency: {0:.4f}\".format(first), \"Hz\")\n",
    "print(\"2nd Frequency: {0:.4f}\".format(second), \"Hz\")\n",
    "print(\"3rd Frequency: {0:.4f}\".format(third), \"Hz\")\n",
    "\n",
    "f1 = np.sqrt(e.real[0])/2/np.pi\n",
    "fn = np.sqrt(e.real[-1])/2/np.pi\n",
    "print('\\nLongest time period = {:1.3f} ms\\nshortest time period = {:1.3f} ms'.format(1/f1*1000,1/fn*1000))\n",
    "\n",
    "#Plot/Labels\n",
    "x = np.linspace(0, L, N)\n",
    "\n",
    "plt.plot(x*10, v[:,0], label = \"First Mode\")\n",
    "plt.plot(x*10, v[:,1], label = \"Second Mode\")\n",
    "plt.plot(x*10, v[:,2], label = \"Third Mode\")\n",
    "plt.xlabel(\"Nodes\")\n",
    "plt.ylabel(\"Displacement (m)\")\n",
    "plt.title(\"30 Nodes\")\n",
    "plt.legend(bbox_to_anchor = (1,0.5), loc='center left');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The First 3 Natural Frequencies of a 45-Element String (Hz):\n",
      "1st Frequency: 196.0404 Hz\n",
      "2nd Frequency: 391.8523 Hz\n",
      "3rd Frequency: 587.2073 Hz\n",
      "\n",
      "Longest time period = 5.101 ms\n",
      "shortest time period = 0.174 ms\n"
     ]
    },
    {
     "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": [
    "#45 Nodes\n",
    "N = 45\n",
    "dx = L/(N+1)\n",
    "k = T/dx**2/mu\n",
    "\n",
    "A = k*(np.diag(np.ones(N)*2)\\\n",
    "       -np.diag(np.ones(N-1),-1)\\\n",
    "       -np.diag(np.ones(N-1),1))\n",
    "\n",
    "e,v = linalg.eig(A)\n",
    "isort = np.argsort(e.real)\n",
    "\n",
    "e = e[isort]\n",
    "v = v[:,isort]\n",
    "\n",
    "first = e.real[0]**0.5/2/np.pi\n",
    "second = e.real[1]**0.5/2/np.pi\n",
    "third = e.real[2]**0.5/2/np.pi\n",
    "\n",
    "print(\"The First 3 Natural Frequencies of a 45-Element String (Hz):\")\n",
    "print(\"1st Frequency: {0:.4f}\".format(first), \"Hz\")\n",
    "print(\"2nd Frequency: {0:.4f}\".format(second), \"Hz\")\n",
    "print(\"3rd Frequency: {0:.4f}\".format(third), \"Hz\")\n",
    "\n",
    "f1 = np.sqrt(e.real[0])/2/np.pi\n",
    "fn = np.sqrt(e.real[-1])/2/np.pi\n",
    "print('\\nLongest time period = {:1.3f} ms\\nshortest time period = {:1.3f} ms'.format(1/f1*1000,1/fn*1000))\n",
    "\n",
    "#Plot/Labels\n",
    "x = np.linspace(0, L, N)\n",
    "\n",
    "plt.plot(x*10, -v[:,0], label = \"First Mode\")\n",
    "plt.plot(x*10, v[:,1], label = \"Second Mode\")\n",
    "plt.plot(x*10, -v[:,2], label = \"Third Mode\")\n",
    "plt.xlabel(\"Nodes\")\n",
    "plt.ylabel(\"Displacement (m)\")\n",
    "plt.title(\"45 Nodes\")\n",
    "plt.legend(bbox_to_anchor = (1,0.5), loc='center left');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The First 3 Natural Frequencies of a 60-Element String (Hz):\n",
      "1st Frequency: 196.0569 Hz\n",
      "2nd Frequency: 391.9837 Hz\n",
      "3rd Frequency: 587.6507 Hz\n",
      "\n",
      "Longest time period = 5.101 ms\n",
      "shortest time period = 0.131 ms\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#60 Nodes\n",
    "N = 60\n",
    "dx = L/(N+1)\n",
    "k = T/dx**2/mu\n",
    "\n",
    "A = k*(np.diag(np.ones(N)*2)\\\n",
    "       -np.diag(np.ones(N-1),-1)\\\n",
    "       -np.diag(np.ones(N-1),1))\n",
    "\n",
    "e,v = linalg.eig(A)\n",
    "isort = np.argsort(e.real)\n",
    "\n",
    "e = e[isort]\n",
    "v = v[:,isort]\n",
    "\n",
    "first = e.real[0]**0.5/2/np.pi\n",
    "second = e.real[1]**0.5/2/np.pi\n",
    "third = e.real[2]**0.5/2/np.pi\n",
    "\n",
    "print(\"The First 3 Natural Frequencies of a 60-Element String (Hz):\")\n",
    "print(\"1st Frequency: {0:.4f}\".format(first), \"Hz\")\n",
    "print(\"2nd Frequency: {0:.4f}\".format(second), \"Hz\")\n",
    "print(\"3rd Frequency: {0:.4f}\".format(third), \"Hz\")\n",
    "\n",
    "f1 = np.sqrt(e.real[0])/2/np.pi\n",
    "fn = np.sqrt(e.real[-1])/2/np.pi\n",
    "print('\\nLongest time period = {:1.3f} ms\\nshortest time period = {:1.3f} ms'.format(1/f1*1000,1/fn*1000))\n",
    "\n",
    "#Plot/Labels\n",
    "x = np.linspace(0, L, N)\n",
    "\n",
    "plt.plot(x*10, v[:,0], label = \"First Mode\")\n",
    "plt.plot(x*10, -v[:,1], label = \"Second Mode\")\n",
    "plt.plot(x*10, v[:,2], label = \"Third Mode\")\n",
    "plt.xlabel(\"Nodes\")\n",
    "plt.ylabel(\"Displacement (m)\")\n",
    "plt.title(\"60 Nodes\")\n",
    "plt.legend(bbox_to_anchor = (1,0.5), loc='center left');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Discussion:__ From the graphs above, we can see that in order for the modes shapes to converge, there needs to be about 45 nodes. Although it appears that convergence takes place after 30 nodes from the graphs, there is still some change in the third frequency when comparing 30 to 45. Thus, we can should say that minimum node count for convergence is 45. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "b. Use the number of nodes necessary for convergence to calculate the first 3 modes of vibration for the other 5 strings on the guitar. Display the first three natural frequencies for all six strings. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "E string Natural Frequencies:\n",
      "1st: 329.64 Hz\n",
      "2nd: 658.89 Hz\n",
      "3rd: 987.37 Hz\n",
      "\n",
      "B string Natural Frequencies:\n",
      "1st: 247.05 Hz\n",
      "2nd: 493.82 Hz\n",
      "3rd: 740.01 Hz\n",
      "\n",
      "G string Natural Frequencies:\n",
      "1st: 196.04 Hz\n",
      "2nd: 391.85 Hz\n",
      "3rd: 587.20 Hz\n",
      "\n",
      "D string Natural Frequencies:\n",
      "1st: 146.89 Hz\n",
      "2nd: 293.60 Hz\n",
      "3rd: 439.97 Hz\n",
      "\n",
      "A string Natural Frequencies:\n",
      "1st: 110.01 Hz\n",
      "2nd: 219.89 Hz\n",
      "3rd: 329.51 Hz\n",
      "\n",
      "E string Natural Frequencies:\n",
      "1st: 82.44 Hz\n",
      "2nd: 164.78 Hz\n",
      "3rd: 246.93 Hz\n",
      "\n"
     ]
    }
   ],
   "source": [
    "N = 45\n",
    "\n",
    "#Create Arrays \n",
    "densities = 0.001*np.array([0.401, 0.708, 1.140, 2.333, 4.466, 6.790])  #kg/m\n",
    "tensions = 9.81*np.array([7.28, 7.22, 7.32, 8.41, 9.03, 7.71])  #N\n",
    "\n",
    "w1 = np.zeros(len(densities))  #1st Frequency\n",
    "w2 = np.zeros(len(densities))  #2nd Frequency\n",
    "w3 = np.zeros(len(densities))  #3rd Frequency\n",
    "\n",
    "for i, (mu, T) in enumerate(zip(densities, tensions)):\n",
    "    dx = L/(N+1)\n",
    "    k = T/dx**2/mu\n",
    "    A = k*(np.diag(np.ones(N)*2)\\\n",
    "           -np.diag(np.ones(N-1), -1)\\\n",
    "           -np.diag(np.ones(N-1), 1))\n",
    "   \n",
    "    e, v = linalg.eig(A)\n",
    "    isort = np.argsort(e.real)\n",
    "    \n",
    "    e = e[isort]\n",
    "    v = v[:, isort]\n",
    "    \n",
    "    w_N = e.real**0.5/2/np.pi\n",
    "    w1[i] = w_N[0]\n",
    "    w2[i] = w_N[1]\n",
    "    w3[i] = w_N[2]\n",
    "    \n",
    "strings = ['E', 'B', 'G', 'D', 'A', 'E']\n",
    "for (string, w1, w2, w3) in zip(strings, w1, w2, w3):\n",
    "    print('{} string Natural Frequencies:'.format(string))\n",
    "    print('1st: {:.2f} Hz'.format(w1))\n",
    "    print('2nd: {:.2f} Hz'.format(w2))\n",
    "    print('3rd: {:.2f} Hz'.format(w3))\n",
    "    print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "c. Create an audio signal that has the 18 frequencies (6 strings $\\times$ 3 modes) in an array and display it using the `from IPython.display import Audio` library. \n",
    "\n",
    "_Hint: you don't need to solve the differential equations here. You can use the calculated frequencies to add sine-waves together:_ $\\sin(f_12\\pi t)+\\sin(f_22\\pi t)+...$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
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     "execution_count": 15,
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   "source": [
    "signal = np.zeros(18)\n",
    "r = 20000\n",
    "\n",
    "tsig = np.arange(0, 3, 1/r)\n",
    "data = 0\n",
    "for i in range(0,18):\n",
    "    data += np.sin(signal[i]*2*np.pi*tsig)\n",
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    "Audio(data=data,rate=r)"
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