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  1. {
  2. "cells": [
  3. {
  4. "cell_type": "code",
  5. "execution_count": 1,
  6. "metadata": {
  7. "collapsed": true,
  8. "deletable": true,
  9. "editable": true
  10. },
  11. "outputs": [],
  12. "source": [
  13. "# Standing Waves Code\n"
  14. ]
  15. },
  16. {
  17. "cell_type": "code",
  18. "execution_count": 2,
  19. "metadata": {
  20. "collapsed": false,
  21. "deletable": true,
  22. "editable": true
  23. },
  24. "outputs": [],
  25. "source": [
  26. "%matplotlib inline\n",
  27. "import numpy as np\n",
  28. "from __future__ import division\n",
  29. "import matplotlib.pyplot as plt\n"
  30. ]
  31. },
  32. {
  33. "cell_type": "code",
  34. "execution_count": 3,
  35. "metadata": {
  36. "collapsed": true,
  37. "deletable": true,
  38. "editable": true
  39. },
  40. "outputs": [],
  41. "source": [
  42. "#data yellow\n",
  43. "m_y = .001455 \n",
  44. "L_y = 1.63\n",
  45. "Ft_y1 = 6.2784\n",
  46. "Ft_y2 = 3.5807\n",
  47. "lamb_y1 = .710\n",
  48. "lamb_y2 = .530\n",
  49. "Em_y = .000005\n",
  50. "EL_y = .002\n",
  51. "EFt_y1 = .049\n",
  52. "EFt_y2 = .049\n",
  53. "Elamb_y1 = .007\n",
  54. "Elamb_y2 = .007"
  55. ]
  56. },
  57. {
  58. "cell_type": "code",
  59. "execution_count": 4,
  60. "metadata": {
  61. "collapsed": true,
  62. "deletable": true,
  63. "editable": true
  64. },
  65. "outputs": [],
  66. "source": [
  67. "#data black\n",
  68. "m_b = .000450\n",
  69. "L_b = 1.15\n",
  70. "Ft_b1 = 2.2563\n",
  71. "Ft_b2 = 1.2753\n",
  72. "lamb_b1 = .70\n",
  73. "lamb_b2 = .54\n",
  74. "Em_b = .000005\n",
  75. "EL_b = .002\n",
  76. "EFt_b1 = .049\n",
  77. "EFt_b2 = .049\n",
  78. "Elamb_b1 = .007\n",
  79. "Elamb_b2 = .007"
  80. ]
  81. },
  82. {
  83. "cell_type": "code",
  84. "execution_count": 5,
  85. "metadata": {
  86. "collapsed": true,
  87. "deletable": true,
  88. "editable": true
  89. },
  90. "outputs": [],
  91. "source": [
  92. "def Frequency_y1(lamb_y1,Ft_y1,m_y,L_y):\n",
  93. " Frequency_y1 = (1/lamb_y1)*(Ft_y1/(m_y/L_y))**(1/2)\n",
  94. " return Frequency_y1\n",
  95. " "
  96. ]
  97. },
  98. {
  99. "cell_type": "code",
  100. "execution_count": 6,
  101. "metadata": {
  102. "collapsed": true,
  103. "deletable": true,
  104. "editable": true
  105. },
  106. "outputs": [],
  107. "source": [
  108. "def Frequency_y2(lamb_y2,Ft_y2,m_y,L_y):\n",
  109. " Frequency_y2 = (1/lamb_y2)*(Ft_y2/(m_y/L_y))**(1/2)\n",
  110. " return Frequency_y2\n",
  111. " "
  112. ]
  113. },
  114. {
  115. "cell_type": "code",
  116. "execution_count": 7,
  117. "metadata": {
  118. "collapsed": true,
  119. "deletable": true,
  120. "editable": true
  121. },
  122. "outputs": [],
  123. "source": [
  124. "def Frequency_b1(lamb_b1,Ft_b1,m_b,L_b):\n",
  125. " Frequency_b1 = (1/lamb_b1)*(Ft_b1/(m_b/L_b))**(1/2)\n",
  126. " return Frequency_b1"
  127. ]
  128. },
  129. {
  130. "cell_type": "code",
  131. "execution_count": 8,
  132. "metadata": {
  133. "collapsed": true,
  134. "deletable": true,
  135. "editable": true
  136. },
  137. "outputs": [],
  138. "source": [
  139. "def Frequency_b2(lamb_b2,Ft_b2,m_b,L_b):\n",
  140. " Frequency_b2 = (1/lamb_b2)*(Ft_b2/(m_b/L_b))**(1/2)\n",
  141. " return Frequency_b2"
  142. ]
  143. },
  144. {
  145. "cell_type": "code",
  146. "execution_count": 9,
  147. "metadata": {
  148. "collapsed": false,
  149. "deletable": true,
  150. "editable": true
  151. },
  152. "outputs": [],
  153. "source": [
  154. "def ErrorFrequency_y1(lamb_y1,Ft_y1, m_y,L_y,Elamb_y1,EFt_y1,Em_y,EL_y,Frequency_y1):\n",
  155. " \n",
  156. " ErrorFrequency_y1 = Frequency_y1*((Elamb_y1/lamb_y1)**2 + ((1/2)*(EFt_y1/Ft_y1))**2 + ((1/2)*(Em_y/m_y))**2 + ((1/2)*(EL_y/L_y))**2 )**(1/2)\n",
  157. " return ErrorFrequency_y1"
  158. ]
  159. },
  160. {
  161. "cell_type": "code",
  162. "execution_count": 10,
  163. "metadata": {
  164. "collapsed": true,
  165. "deletable": true,
  166. "editable": true
  167. },
  168. "outputs": [],
  169. "source": [
  170. "def ErrorFrequency_y2(lamb_y2,Ft_y2, m_y,L_y,Elamb_y2,EFt_y2,Em_y,EL_y,Frequency_y2):\n",
  171. " ErrorFrequency_y2 = Frequency_y2*((Elamb_y2/lamb_y2)**2 + ((1/2)*(EFt_y2/Ft_y2))**2 + ((1/2)*(Em_y/m_y))**2 + ((1/2)*(EL_y/L_y))**2 )**(1/2)\n",
  172. " return ErrorFrequency_y2"
  173. ]
  174. },
  175. {
  176. "cell_type": "code",
  177. "execution_count": 11,
  178. "metadata": {
  179. "collapsed": true,
  180. "deletable": true,
  181. "editable": true
  182. },
  183. "outputs": [],
  184. "source": [
  185. "def ErrorFrequency_b1(lamb_b1,Ft_b1, m_b,L_b,Elamb_b1,EFt_b1,Em_b,EL_b,Frequency_b1):\n",
  186. " ErrorFrequency_b1 = Frequency_b1*((Elamb_b1/lamb_b1)**2 + ((1/2)*(EFt_b1/Ft_b1))**2 + ((1/2)*(Em_b/m_b))**2 + ((1/2)*(EL_b/L_b))**2 )**(1/2)\n",
  187. " return ErrorFrequency_b1"
  188. ]
  189. },
  190. {
  191. "cell_type": "code",
  192. "execution_count": 12,
  193. "metadata": {
  194. "collapsed": true,
  195. "deletable": true,
  196. "editable": true
  197. },
  198. "outputs": [],
  199. "source": [
  200. "def ErrorFrequency_b2(lamb_b2,Ft_b2, m_b,L_b,Elamb_b2,EFt_b2,Em_b,EL_b,Frequency_b2):\n",
  201. " ErrorFrequency_b2 = Frequency_b2*((Elamb_b2/lamb_b2)**2 + ((1/2)*(EFt_b2/Ft_b2))**2 + ((1/2)*(Em_b/m_b))**2 + ((1/2)*(EL_b/L_b))**2 )**(1/2)\n",
  202. " return ErrorFrequency_b2"
  203. ]
  204. },
  205. {
  206. "cell_type": "code",
  207. "execution_count": 13,
  208. "metadata": {
  209. "collapsed": false,
  210. "deletable": true,
  211. "editable": true
  212. },
  213. "outputs": [
  214. {
  215. "name": "stdout",
  216. "output_type": "stream",
  217. "text": [
  218. "Frequency Yellow 3rd Harmonic = 118.12136242 Hz\n",
  219. "Frequency Yellow 4th Harmonic = 119.500687565 Hz\n",
  220. "Frequency black 3rd Harmonic = 108.478343555 Hz\n",
  221. "Frequency black 4th Harmonic = 105.719495823 Hz\n"
  222. ]
  223. }
  224. ],
  225. "source": [
  226. "print \"Frequency Yellow 3rd Harmonic = \",Frequency_y1(lamb_y1,Ft_y1,m_y,L_y), \"Hz\"\n",
  227. "freqy1 = Frequency_y1(lamb_y1,Ft_y1,m_y,L_y)\n",
  228. "print \"Frequency Yellow 4th Harmonic = \", Frequency_y2(lamb_y2,Ft_y2,m_y,L_y), \"Hz\"\n",
  229. "freqy2 = Frequency_y2(lamb_y2,Ft_y2,m_y,L_y)\n",
  230. "print \"Frequency black 3rd Harmonic = \", Frequency_b1(lamb_b1,Ft_b1,m_b,L_b), \"Hz\"\n",
  231. "freqb1 = Frequency_b1(lamb_b1,Ft_b1,m_b,L_b)\n",
  232. "print \"Frequency black 4th Harmonic = \", Frequency_b2(lamb_b2,Ft_b2,m_b,L_b), \"Hz\"\n",
  233. "freqb2 = Frequency_b2(lamb_b2,Ft_b2,m_b,L_b)"
  234. ]
  235. },
  236. {
  237. "cell_type": "code",
  238. "execution_count": 14,
  239. "metadata": {
  240. "collapsed": false,
  241. "deletable": true,
  242. "editable": true
  243. },
  244. "outputs": [
  245. {
  246. "name": "stdout",
  247. "output_type": "stream",
  248. "text": [
  249. "Error in Frequency Yellow 3rd Harmonic = 1.27088522636 Hz\n",
  250. "Error in Frequency Yellow 4th Harmonic = 1.79085307487 Hz\n",
  251. "Error in Frequency Black 3rd Harmonic = 1.71357001035 Hz\n",
  252. "Error in Frequency Black 4th Harmonic = 2.52119974452 Hz\n"
  253. ]
  254. }
  255. ],
  256. "source": [
  257. "print \"Error in Frequency Yellow 3rd Harmonic =\",ErrorFrequency_y1(lamb_y1,Ft_y1, m_y,L_y,Elamb_y1,EFt_y1,Em_y,EL_y,freqy1), \"Hz\"\n",
  258. "print \"Error in Frequency Yellow 4th Harmonic =\",ErrorFrequency_y2(lamb_y2,Ft_y2, m_y,L_y,Elamb_y2,EFt_y2,Em_y,EL_y,freqy2), \"Hz\"\n",
  259. "print \"Error in Frequency Black 3rd Harmonic =\",ErrorFrequency_b1(lamb_b1,Ft_b1, m_b,L_b,Elamb_b1,EFt_b1,Em_b,EL_b,freqb1), \"Hz\"\n",
  260. "print \"Error in Frequency Black 4th Harmonic =\",ErrorFrequency_b2(lamb_b2,Ft_b2, m_b,L_b,Elamb_b2,EFt_b2,Em_b,EL_b,freqb2), \"Hz\"\n"
  261. ]
  262. },
  263. {
  264. "cell_type": "code",
  265. "execution_count": 15,
  266. "metadata": {
  267. "collapsed": false,
  268. "deletable": true,
  269. "editable": true
  270. },
  271. "outputs": [
  272. {
  273. "name": "stdout",
  274. "output_type": "stream",
  275. "text": [
  276. "Frequency Yellow 3rd Harmonic = 118.12136242 +/_ 1.27088522636\n",
  277. "Frequency Yellow 4th Harmonic = 119.500687565 +/_ 1.79085307487\n",
  278. "Frequency Yellow 3rd Harmonic = 108.478343555 +/_ 1.71357001035\n",
  279. "Frequency Yellow 3rd Harmonic = 105.719495823 +/_ 2.52119974452\n"
  280. ]
  281. }
  282. ],
  283. "source": [
  284. "print \"Frequency Yellow 3rd Harmonic =\",Frequency_y1(lamb_y1,Ft_y1,m_y,L_y),\"+/_\",ErrorFrequency_y1(lamb_y1,Ft_y1, m_y,L_y,Elamb_y1,EFt_y1,Em_y,EL_y,freqy1)\n",
  285. "print \"Frequency Yellow 4th Harmonic =\",Frequency_y2(lamb_y2,Ft_y2,m_y,L_y),\"+/_\",ErrorFrequency_y2(lamb_y2,Ft_y2, m_y,L_y,Elamb_y2,EFt_y2,Em_y,EL_y,freqy2)\n",
  286. "print \"Frequency Yellow 3rd Harmonic =\",Frequency_b1(lamb_b1,Ft_b1,m_b,L_b),\"+/_\",ErrorFrequency_b1(lamb_b1,Ft_b1, m_b,L_b,Elamb_b1,EFt_b1,Em_b,EL_b,freqb1)\n",
  287. "print \"Frequency Yellow 3rd Harmonic =\",Frequency_b2(lamb_b2,Ft_b2,m_b,L_b),\"+/_\",ErrorFrequency_b2(lamb_b2,Ft_b2, m_b,L_b,Elamb_b2,EFt_b2,Em_b,EL_b,freqb2)\n"
  288. ]
  289. }
  290. ],
  291. "metadata": {
  292. "kernelspec": {
  293. "display_name": "Python 2",
  294. "language": "python",
  295. "name": "python2"
  296. },
  297. "language_info": {
  298. "codemirror_mode": {
  299. "name": "ipython",
  300. "version": 2
  301. },
  302. "file_extension": ".py",
  303. "mimetype": "text/x-python",
  304. "name": "python",
  305. "nbconvert_exporter": "python",
  306. "pygments_lexer": "ipython2",
  307. "version": "2.7.13"
  308. }
  309. },
  310. "nbformat": 4,
  311. "nbformat_minor": 2
  312. }
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