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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Computational Mechanics Boundary Values - Project 05\n",
"\n",
"![6-string guitar diagram](../images/guitar.png)"
]
},
{
"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",
"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": 89,
"metadata": {},
"outputs": [
{
"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": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"plt.rcParams.update({'font.size': 22})\n",
"plt.rcParams['lines.linewidth'] = 3\n",
"\n",
"L = 0.64 #m\n",
"E = 10e9 #Pa\n",
"I = ((4*(2**3))/12)*(10**-8) #m^4\n",
"height = 0.004 #m\n",
"g = 9.81 #m/s^2\n",
"\n",
"#density in g/m\n",
"density_e1 = 0.401\n",
"density_b = 0.708\n",
"density_g = 1.140\n",
"density_d = 2.333\n",
"density_a = 4.466\n",
"density_e2 = 6.790\n",
"\n",
"#tension in g\n",
"tension_e1 = 7.28e3\n",
"tension_b = 7.22e3\n",
"tension_g = 7.32e3\n",
"tension_d = 8.41e3\n",
"tension_a = 9.03e3\n",
"tension_e2 = 7.71e3\n",
"\n",
"#moment in g*m^2/s^2\n",
"M = (tension_e1 + tension_b + tension_g + tension_d + tension_a + tension_e2)*g*height\n",
"\n",
"h = L/6\n",
"\n",
"A=np.diag(np.ones(6)*6)\\\n",
"+np.diag(np.ones(5)*-4,-1)\\\n",
"+np.diag(np.ones(5)*-4,1)\\\n",
"+np.diag(np.ones(4),-2)\\\n",
"+np.diag(np.ones(4),2)\n",
"A[0,0]+=1\n",
"A[-1,-1]-=5\n",
"A[-2,-1]+=2\n",
"A[-1,-2]+=2\n",
"A[-2,-2]-=1\n",
"\n",
"b=np.zeros(6)\n",
"b[-1]+=(M*(h**2))/(E*I)\n",
"b[-2]-=(M*(h**2))/(E*I)\n",
"\n",
"\n",
"w=np.linalg.solve(A,b)\n",
"xnum=np.arange(0,L+h/2,h)\n",
"\n",
"x=np.linspace(0,L)\n",
"w_an= (M*(x**2))/(2*E*I)\n",
"\n",
"plt.plot(xnum,np.block([0,w]),'s', label='finite')\n",
"plt.plot(x,w_an, label='analytical')\n",
"plt.xlabel('Length (m)')\n",
"plt.ylabel('Deflection (mm)')\n",
"plt.title('Finite Difference: Deflection of Guitar Bridge \\n h=L/6')\n",
"plt.legend(bbox_to_anchor=(1,0.5),loc='center left');"
]
},
{
"cell_type": "code",
"execution_count": 90,
"metadata": {},
"outputs": [
{
"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": [
"h = L/60\n",
"\n",
"A=np.diag(np.ones(60)*6)\\\n",
"+np.diag(np.ones(59)*-4,-1)\\\n",
"+np.diag(np.ones(59)*-4,1)\\\n",
"+np.diag(np.ones(58),-2)\\\n",
"+np.diag(np.ones(58),2)\n",
"A[0,0]+=1\n",
"A[-1,-1]-=5\n",
"A[-2,-1]+=2\n",
"A[-1,-2]+=2\n",
"A[-2,-2]-=1\n",
"\n",
"b=np.zeros(60)\n",
"b[-1]+=(M*(h**2))/(E*I)\n",
"b[-2]-=(M*(h**2))/(E*I)\n",
"\n",
"\n",
"w=np.linalg.solve(A,b)\n",
"xnum=np.arange(0,L+h/2,h)\n",
"\n",
"x=np.linspace(0,L)\n",
"w_an= (M*(x**2))/(2*E*I)\n",
"\n",
"plt.plot(xnum,np.block([0,w]),'s', label='finite')\n",
"plt.plot(x,w_an, label='analytical')\n",
"plt.xlabel('Length (m)')\n",
"plt.ylabel('Deflection (mm)')\n",
"plt.ylim(0,1.5)\n",
"plt.title('Finite Difference: Deflection of Guitar Bridge \\n h=L/60')\n",
"plt.legend(bbox_to_anchor=(1,0.5),loc='center left');"
]
},
{
"cell_type": "code",
"execution_count": 91,
"metadata": {},
"outputs": [
{
"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": [
"h = L/600\n",
"\n",
"A=np.diag(np.ones(600)*6)\\\n",
"+np.diag(np.ones(599)*-4,-1)\\\n",
"+np.diag(np.ones(599)*-4,1)\\\n",
"+np.diag(np.ones(598),-2)\\\n",
"+np.diag(np.ones(598),2)\n",
"A[0,0]+=1\n",
"A[-1,-1]-=5\n",
"A[-2,-1]+=2\n",
"A[-1,-2]+=2\n",
"A[-2,-2]-=1\n",
"\n",
"b=np.zeros(600)\n",
"b[-1]+=(M*(h**2))/(E*I)\n",
"b[-2]-=(M*(h**2))/(E*I)\n",
"\n",
"\n",
"w=np.linalg.solve(A,b)\n",
"xnum=np.arange(0,L+h/2,h)\n",
"\n",
"x=np.linspace(0,L)\n",
"w_an= (M*(x**2))/(2*E*I)\n",
"\n",
"plt.plot(xnum,np.block([0,w]),'s', label='finite')\n",
"plt.plot(x,w_an, label='analytical')\n",
"plt.xlabel('Length (m)')\n",
"plt.ylabel('Deflection (mm)')\n",
"plt.title('Finite Difference: Deflection of Guitar Bridge \\n h=L/600')\n",
"plt.legend(bbox_to_anchor=(1,0.5),loc='center left');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"2. Here we will record the first three frequencies of the 6-string guitar. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"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": 130,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"First, Second, and Third Natural frequencies of 6-element string (Hz)\n",
"[194.43708661 379.1242858 544.80061022]\n",
"\n",
"First, Second, and Third Natural frequencies of 30-element string (Hz)\n",
"[195.99464595 391.48617646 585.97276757]\n",
"\n",
"First, Second, and Third Natural frequencies of 45-element string (Hz)\n",
"[196.04043699 391.85229959 587.20727994]\n",
"\n",
"First, Second, and Third Natural frequencies of 60-element string (Hz)\n",
"[196.05687232 391.9837462 587.65070938]\n"
]
}
],
"source": [
"from scipy import linalg\n",
"\n",
"L = 0.64 #m\n",
"mu = 1.14e-3 #kg/m\n",
"T = 71.81 #N\n",
"\n",
"N1=6\n",
"dx1=L/(N1+1)\n",
"N2=30 \n",
"dx2=L/(N2+1)\n",
"N3=45 \n",
"dx3=L/(N3+1)\n",
"N4=60 \n",
"dx4=L/(N4+1)\n",
"\n",
"k1 = T/dx1**2/mu\n",
"k2 = T/dx2**2/mu\n",
"k3 = T/dx3**2/mu\n",
"k4 = T/dx4**2/mu\n",
"\n",
"A1 = k1*(np.diag(np.ones(N1)*2)\\\n",
" -np.diag(np.ones(N1-1),-1)\\\n",
" -np.diag(np.ones(N1-1),1))\n",
"A2 = k2*(np.diag(np.ones(N2)*2)\\\n",
" -np.diag(np.ones(N2-1),-1)\\\n",
" -np.diag(np.ones(N2-1),1))\n",
"A3 = k3*(np.diag(np.ones(N3)*2)\\\n",
" -np.diag(np.ones(N3-1),-1)\\\n",
" -np.diag(np.ones(N3-1),1))\n",
"A4 = k4*(np.diag(np.ones(N4)*2)\\\n",
" -np.diag(np.ones(N4-1),-1)\\\n",
" -np.diag(np.ones(N4-1),1))\n",
"\n",
"e1,v1=linalg.eig(A1)\n",
"isort1 = np.argsort(e1.real)\n",
"e1=e1.real[isort1]\n",
"v1=v1.real[:,isort1]\n",
"e2,v2=linalg.eig(A2)\n",
"isort2 = np.argsort(e2.real)\n",
"e2=e2.real[isort2]\n",
"v2=v2.real[:,isort2]\n",
"e3,v3=linalg.eig(A3)\n",
"isort3 = np.argsort(e3.real)\n",
"e3=e3.real[isort3]\n",
"v3=v3.real[:,isort3]\n",
"e4,v4=linalg.eig(A4)\n",
"isort4 = np.argsort(e4.real)\n",
"e4=e4.real[isort4]\n",
"v4=v4.real[:,isort4]\n",
"\n",
"print('First, Second, and Third Natural frequencies of {}-element string (Hz)'.format(N1))\n",
"print(e1.real[:3]**0.5/2/np.pi)\n",
"print('\\nFirst, Second, and Third Natural frequencies of {}-element string (Hz)'.format(N2))\n",
"print(e2.real[:3]**0.5/2/np.pi)\n",
"print('\\nFirst, Second, and Third Natural frequencies of {}-element string (Hz)'.format(N3))\n",
"print(e3.real[:3]**0.5/2/np.pi)\n",
"print('\\nFirst, Second, and Third Natural frequencies of {}-element string (Hz)'.format(N4))\n",
"print(e4.real[:3]**0.5/2/np.pi)"
]
},
{
"cell_type": "code",
"execution_count": 131,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"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": [
"plt.figure()\n",
"x1 = np.linspace(0,L,N1+2)\n",
"plt.plot(x1[1:-1],-v1[:,0]/np.max(-v1[:,0]), '-', label='6 nodes')\n",
"x2 = np.linspace(0,L,N2+2)\n",
"plt.plot(x2[1:-1],-v2[:,0]/np.max(-v2[:,0]), '--', label='30 nodes')\n",
"x3 = np.linspace(0,L,N3+2)\n",
"plt.plot(x3[1:-1],v3[:,0]/np.max(v3[:,0]), '*', label='45 nodes')\n",
"x4 = np.linspace(0,L,N4+2)\n",
"plt.plot(x4[1:-1],-v4[:,0]/np.max(-v4[:,0]), '.', label='60 nodes')\n",
"plt.legend(bbox_to_anchor=(1,0.5),loc='center left')\n",
"plt.title('First Mode');\n",
"\n",
"plt.figure()\n",
"x1 = np.linspace(0,L,N1+2)\n",
"plt.plot(x1[1:-1],v1[:,1]/np.max(-v1[:,0]), '-', label='6 nodes')\n",
"x2 = np.linspace(0,L,N2+2)\n",
"plt.plot(x2[1:-1],-v2[:,1]/np.max(-v2[:,0]), '--', label='30 nodes')\n",
"x3 = np.linspace(0,L,N3+2)\n",
"plt.plot(x3[1:-1],v3[:,1]/np.max(v3[:,0]), '*', label='45 nodes')\n",
"x4 = np.linspace(0,L,N4+2)\n",
"plt.plot(x4[1:-1],-v4[:,1]/np.max(-v4[:,0]), '.', label='60 nodes')\n",
"plt.legend(bbox_to_anchor=(1,0.5),loc='center left')\n",
"plt.title('Second Mode');\n",
"\n",
"plt.figure()\n",
"x1 = np.linspace(0,L,N1+2)\n",
"plt.plot(x1[1:-1],-v1[:,2]/np.max(-v1[:,0]), '-', label='6 nodes')\n",
"x2 = np.linspace(0,L,N2+2)\n",
"plt.plot(x2[1:-1],-v2[:,2]/np.max(-v2[:,0]), '--', label='30 nodes')\n",
"x3 = np.linspace(0,L,N3+2)\n",
"plt.plot(x3[1:-1],v3[:,2]/np.max(v3[:,0]), '*', label='45 nodes')\n",
"x4 = np.linspace(0,L,N4+2)\n",
"plt.plot(x4[1:-1],-v4[:,2]/np.max(-v4[:,0]), '.', label='60 nodes')\n",
"plt.legend(bbox_to_anchor=(1,0.5),loc='center left')\n",
"plt.title('Third Mode');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For the first three modes, using 60 nodes provides the best convergence."
]
},
{
"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": "code",
"execution_count": 132,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"First, Second, and Third Natural frequencies of 60-element E1 string (Hz)\n",
"[329.6628732 659.1071585 988.11441292]\n",
"\n",
"First, Second, and Third Natural frequencies of 60-element B string (Hz)\n",
"[247.07483046 493.98583425 740.56929334]\n",
"\n",
"First, Second, and Third Natural frequencies of 60-element G string (Hz)\n",
"[196.05578023 391.98156274 587.64743601]\n",
"\n",
"First, Second, and Third Natural frequencies of 60-element D string (Hz)\n",
"[146.89843351 293.69946381 440.30575228]\n",
"\n",
"First, Second, and Third Natural frequencies of 60-element A string (Hz)\n",
"[110.01731758 219.96168654 329.7602066 ]\n",
"\n",
"First, Second, and Third Natural frequencies of 60-element E2 string (Hz)\n",
"[ 82.44585724 164.83704751 247.11894012]\n"
]
}
],
"source": [
"N = 60\n",
"dx = L/(N+1)\n",
"\n",
"T_e1 = tension_e1*g*(10**-3)\n",
"T_b = tension_b*g*(10**-3)\n",
"T_g = tension_g*g*(10**-3)\n",
"T_d = tension_d*g*(10**-3)\n",
"T_a = tension_a*g*(10**-3)\n",
"T_e2 = tension_e2*g*(10**-3)\n",
"\n",
"mu_e1 = density_e1*(10**-3)\n",
"mu_b = density_b*(10**-3)\n",
"mu_g = density_g*(10**-3)\n",
"mu_d = density_d*(10**-3)\n",
"mu_a = density_a*(10**-3)\n",
"mu_e2 = density_e2*(10**-3)\n",
"\n",
"k_e1 = T_e1/dx**2/mu_e1\n",
"k_b = T_b/dx**2/mu_b\n",
"k_g = T_g/dx**2/mu_g\n",
"k_d = T_d/dx**2/mu_d\n",
"k_a = T_a/dx**2/mu_a\n",
"k_e2 = T_e2/dx**2/mu_e2\n",
"\n",
"A_e1 = k_e1*(np.diag(np.ones(N)*2)\\\n",
" -np.diag(np.ones(N-1),-1)\\\n",
" -np.diag(np.ones(N-1),1))\n",
"A_b = k_b*(np.diag(np.ones(N)*2)\\\n",
" -np.diag(np.ones(N-1),-1)\\\n",
" -np.diag(np.ones(N-1),1))\n",
"A_g = k_g*(np.diag(np.ones(N)*2)\\\n",
" -np.diag(np.ones(N-1),-1)\\\n",
" -np.diag(np.ones(N-1),1))\n",
"A_d = k_d*(np.diag(np.ones(N)*2)\\\n",
" -np.diag(np.ones(N-1),-1)\\\n",
" -np.diag(np.ones(N-1),1))\n",
"A_a = k_a*(np.diag(np.ones(N)*2)\\\n",
" -np.diag(np.ones(N-1),-1)\\\n",
" -np.diag(np.ones(N-1),1))\n",
"A_e2 = k_e2*(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_e1,v_e1=linalg.eig(A_e1)\n",
"isort_e1 = np.argsort(e_e1.real)\n",
"e_e1=e_e1.real[isort_e1]\n",
"v_e1=v_e1.real[:,isort_e1]\n",
"e_b,v_b=linalg.eig(A_b)\n",
"isort_b = np.argsort(e_b.real)\n",
"e_b=e_b.real[isort_b]\n",
"v_b=v_b.real[:,isort_b]\n",
"e_g,v_g=linalg.eig(A_g)\n",
"isort_g = np.argsort(e_g.real)\n",
"e_g=e_g.real[isort_g]\n",
"v_g=v_g.real[:,isort_g]\n",
"e_d,v_d=linalg.eig(A_d)\n",
"isort_d = np.argsort(e_d.real)\n",
"e_d=e_d.real[isort_d]\n",
"v_d=v_d.real[:,isort_d]\n",
"e_a,v_a=linalg.eig(A_a)\n",
"isort_a = np.argsort(e_a.real)\n",
"e_a=e_a.real[isort_a]\n",
"v_a=v_a.real[:,isort_a]\n",
"e_e2,v_e2=linalg.eig(A_e2)\n",
"isort_e2 = np.argsort(e_e2.real)\n",
"e_e2=e_e2.real[isort_e2]\n",
"v_e2=v_e2.real[:,isort_e2]\n",
"\n",
"print('First, Second, and Third Natural frequencies of {}-element E1 string (Hz)'.format(N))\n",
"print(e_e1.real[:3]**0.5/2/np.pi)\n",
"print('\\nFirst, Second, and Third Natural frequencies of {}-element B string (Hz)'.format(N))\n",
"print(e_b.real[:3]**0.5/2/np.pi)\n",
"print('\\nFirst, Second, and Third Natural frequencies of {}-element G string (Hz)'.format(N))\n",
"print(e_g.real[:3]**0.5/2/np.pi)\n",
"print('\\nFirst, Second, and Third Natural frequencies of {}-element D string (Hz)'.format(N))\n",
"print(e_d.real[:3]**0.5/2/np.pi)\n",
"print('\\nFirst, Second, and Third Natural frequencies of {}-element A string (Hz)'.format(N))\n",
"print(e_a.real[:3]**0.5/2/np.pi)\n",
"print('\\nFirst, Second, and Third Natural frequencies of {}-element E2 string (Hz)'.format(N))\n",
"print(e_e2.real[:3]**0.5/2/np.pi)"
]
},
{
"cell_type": "code",
"execution_count": 133,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"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": [
"plt.figure()\n",
"x_e1 = np.linspace(0,L,N+2)\n",
"plt.plot(x_e1[1:-1],-v_e1[:,0]/np.max(-v_e1[:,0]), '-', label='E1')\n",
"x_b = np.linspace(0,L,N+2)\n",
"plt.plot(x_b[1:-1],-v_b[:,0]/np.max(-v_b[:,0]), '--', label='B')\n",
"x_g = np.linspace(0,L,N+2)\n",
"plt.plot(x_g[1:-1],-v_g[:,0]/np.max(-v_g[:,0]), '*', label='G')\n",
"x_d = np.linspace(0,L,N+2)\n",
"plt.plot(x_d[1:-1],-v_d[:,0]/np.max(-v_d[:,0]), '.', label='D')\n",
"x_a = np.linspace(0,L,N+2)\n",
"plt.plot(x_a[1:-1],v_a[:,0]/np.max(v_a[:,0]), '*', label='A')\n",
"x_e2 = np.linspace(0,L,N+2)\n",
"plt.plot(x_e2[1:-1],-v_e2[:,0]/np.max(-v_e2[:,0]), '.', label='E2')\n",
"plt.legend(bbox_to_anchor=(1,0.5),loc='center left')\n",
"plt.title('First Mode');\n",
"\n",
"plt.figure()\n",
"x_e1 = np.linspace(0,L,N+2)\n",
"plt.plot(x_e1[1:-1],-v_e1[:,1]/np.max(-v_e1[:,0]), '-', label='E1')\n",
"x_b = np.linspace(0,L,N+2)\n",
"plt.plot(x_b[1:-1],-v_b[:,1]/np.max(-v_b[:,0]), '--', label='B')\n",
"x_g = np.linspace(0,L,N+2)\n",
"plt.plot(x_g[1:-1],-v_g[:,1]/np.max(-v_g[:,0]), '*', label='G')\n",
"x_d = np.linspace(0,L,N+2)\n",
"plt.plot(x_d[1:-1],-v_d[:,1]/np.max(-v_d[:,0]), '.', label='D')\n",
"x_a = np.linspace(0,L,N+2)\n",
"plt.plot(x_a[1:-1],v_a[:,1]/np.max(v_a[:,0]), '*', label='A')\n",
"x_e2 = np.linspace(0,L,N+2)\n",
"plt.plot(x_e2[1:-1],-v_e2[:,1]/np.max(-v_e2[:,0]), '.', label='E2')\n",
"plt.legend(bbox_to_anchor=(1,0.5),loc='center left')\n",
"plt.title('Second Mode');\n",
"\n",
"plt.figure()\n",
"x_e1 = np.linspace(0,L,N+2)\n",
"plt.plot(x_e1[1:-1],-v_e1[:,2]/np.max(-v_e1[:,0]), '-', label='E1')\n",
"x_b = np.linspace(0,L,N+2)\n",
"plt.plot(x_b[1:-1],-v_b[:,2]/np.max(-v_b[:,0]), '--', label='B')\n",
"x_g = np.linspace(0,L,N+2)\n",
"plt.plot(x_g[1:-1],-v_g[:,2]/np.max(-v_g[:,0]), '*', label='G')\n",
"x_d = np.linspace(0,L,N+2)\n",
"plt.plot(x_d[1:-1],-v_d[:,2]/np.max(-v_d[:,0]), '.', label='D')\n",
"x_a = np.linspace(0,L,N+2)\n",
"plt.plot(x_a[1:-1],v_a[:,2]/np.max(v_a[:,0]), '*', label='A')\n",
"x_e2 = np.linspace(0,L,N+2)\n",
"plt.plot(x_e2[1:-1],-v_e2[:,2]/np.max(-v_e2[:,0]), '.', label='E2')\n",
"plt.legend(bbox_to_anchor=(1,0.5),loc='center left')\n",
"plt.title('Third Mode');"
]
},
{
"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": 144,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
" <audio controls=\"controls\" >\n",
" <source 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\" type=\"audio/wav\" />\n",
" Your browser does not support the audio element.\n",
" </audio>\n",
" "
],
"text/plain": [
"<IPython.lib.display.Audio object>"
]
},
"execution_count": 144,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from IPython.display import Audio\n",
"\n",
"frequency = np.array([(e_e1.real[:3]**0.5/2/np.pi)[0],\n",
" (e_e1.real[:3]**0.5/2/np.pi)[1],\n",
" (e_e1.real[:3]**0.5/2/np.pi)[2],\n",
" (e_b.real[:3]**0.5/2/np.pi)[0],\n",
" (e_b.real[:3]**0.5/2/np.pi)[1],\n",
" (e_b.real[:3]**0.5/2/np.pi)[2],\n",
" (e_g.real[:3]**0.5/2/np.pi)[0],\n",
" (e_g.real[:3]**0.5/2/np.pi)[1],\n",
" (e_g.real[:3]**0.5/2/np.pi)[2],\n",
" (e_d.real[:3]**0.5/2/np.pi)[0],\n",
" (e_d.real[:3]**0.5/2/np.pi)[1],\n",
" (e_d.real[:3]**0.5/2/np.pi)[2],\n",
" (e_a.real[:3]**0.5/2/np.pi)[0],\n",
" (e_a.real[:3]**0.5/2/np.pi)[1],\n",
" (e_a.real[:3]**0.5/2/np.pi)[2],\n",
" (e_e2.real[:3]**0.5/2/np.pi)[0],\n",
" (e_e2.real[:3]**0.5/2/np.pi)[1],\n",
" (e_e2.real[:3]**0.5/2/np.pi)[2]])\n",
"\n",
"N = 15000\n",
"dt = 3/N\n",
"t = np.linspace(0,3,N)\n",
"samplerate = int(1/dt)\n",
"\n",
"out_file=np.sin(2*np.pi*frequency[0]*t)\n",
"for i in range(1,18):\n",
" out_file += np.sin(2*np.pi*frequency[i]*t)\n",
"\n",
"Audio(data=out_file,rate=samplerate)"
]
},
{
"cell_type": "code",
"execution_count": 142,
"metadata": {},
"outputs": [
{
"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": [
"plt.plot(np.arange(0,len(out_file))*dt*1000,out_file)\n",
"plt.xlim((0,200))\n",
"plt.xlabel('time (ms)')\n",
"plt.ylabel('input signal (a.u.)');"
]
},
{
"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",
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