{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 2 - What is Light"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 2 - pg 32"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Space profile of a wave y= 2*sin(10*pi*t - (pi*x)/40 + pi/4) when  t= T/4\n",
      "\n",
      "\n",
      "\tx (in m) \t y1(x)  (in m)\n",
      "\n",
      "\t0.0 \t\t1.41421356237 \n",
      "\n",
      "\t10.0 \t\t2.0 \n",
      "\n",
      "\t20.0 \t\t1.41421356237 \n",
      "\n",
      "\t30.0 \t\t0.0 \n",
      "\n",
      "\t40.0 \t\t-1.41421356237 \n",
      "\n",
      "\t50.0 \t\t-2.0 \n",
      "\n",
      "\t60.0 \t\t-1.41421356237 \n",
      "\n",
      "\t70.0 \t\t-2.44929359829e-16 \n",
      "\n",
      "\t80.0 \t\t1.41421356237 \n",
      "\n",
      "\t90.0 \t\t2.0 \n",
      "\n",
      "\t100.0 \t\t1.41421356237 \n",
      "\n",
      "\t110.0 \t\t2.26621555906e-15 \n",
      "\n",
      "\t120.0 \t\t-1.41421356237 \n",
      "\n",
      "\t130.0 \t\t-2.0 \n",
      "\n",
      "\t140.0 \t\t-1.41421356237 \n",
      "\n",
      "\t150.0 \t\t-7.34788079488e-16 \n",
      "\n",
      "\t160.0 \t\t1.41421356237 \n",
      "\n",
      "\t170.0 \t\t2.0 \n",
      "\n"
     ]
    },
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       "YDqO4zhOC7jBdBzHcZwWcIPpOI7jOC3w/wHIGArraLdQJwAAAABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x58a2290>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The time profile of a wave y= 2*sin(10*pi*t - (pi*x)/40 + pi/4) when  x= lambd/8\n",
      "\n",
      "\n",
      "\t t(in s)     \t     y2(t) (in m)\n",
      "\n",
      "\n",
      "\t10.0 \t\t0.0 \n",
      "\n",
      "\t10.0 \t\t1.41421356237 \n",
      "\n",
      "\t10.0 \t\t2.0 \n",
      "\n",
      "\t10.0 \t\t1.41421356237 \n",
      "\n",
      "\t10.0 \t\t2.44929359829e-16 \n",
      "\n",
      "\t10.0 \t\t-1.41421356237 \n",
      "\n",
      "\t10.0 \t\t-2.0 \n",
      "\n",
      "\t10.0 \t\t-1.41421356237 \n",
      "\n",
      "\t10.0 \t\t-2.26621555906e-15 \n",
      "\n",
      "\t10.0 \t\t1.41421356237 \n",
      "\n",
      "\t10.0 \t\t2.0 \n",
      "\n",
      "\t10.0 \t\t1.41421356237 \n",
      "\n",
      "\t10.0 \t\t7.34788079488e-16 \n",
      "\n",
      "\t10.0 \t\t-1.41421356237 \n",
      "\n",
      "\t10.0 \t\t-2.0 \n",
      "\n",
      "\t10.0 \t\t-1.41421356237 \n",
      "\n"
     ]
    },
    {
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       "AAAASUVORK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x80a9750>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plot the required space and time profiles\n",
    "%matplotlib inline\n",
    "# wave y= 2*sin(10*pi*t - (pi*x)/40  + pi/4)\n",
    "# (a) Plot the space profile at t= T/4\n",
    "# Comapring the given Equation with  y= A*sin(omega*t - k*x + phi)\n",
    "#given\n",
    "import math,matplotlib,numpy\n",
    "from matplotlib import pyplot\n",
    "omega = 10*math.pi ; #Angular frequency in rad/s\n",
    "k= math.pi/40. ; # Wave number in rad/m\n",
    "T= 1/5. ; # 2*pi/T = 10*pi , so Time period is 1/5 s\n",
    "lambd = 80.; # Wavelength in m ,  2*pi/lambd = pi/40 , so lambd = 80\n",
    "#calculations\n",
    "t1= T/4; #time period in s\n",
    "x1= 0.;#  in m\n",
    "print\"The Space profile of a wave y= 2*sin(10*pi*t - (pi*x)/40 + pi/4) when  t= T/4\\n\\n\"\n",
    "print\"\\tx (in m) \\t y1(x)  (in m)\\n\"\n",
    "while x1<180:\n",
    "\ty1= 2*math.sin((omega*t1)-(k*x1)+ (math.pi/4));\n",
    "\tprint\"\\t\",x1,\"\\t\\t\",y1,\"\\n\"\n",
    "\tx1 = x1+10;\n",
    "\n",
    "#Now, we will plot the space profile from the values obtained for y1 for each value of x1\n",
    "x_1 = numpy.array([0,10.,20.,30.,40.,50.,60.,70.,80.,90.,100.,110.,120.,130.,140.,150.,160.,170.]);\n",
    "y_1 = numpy.array([1.414214,2.000000,1.414214,0.000000,-1.414214,-2.000000,-1.414214,-0.000000,1.414214,2.000000,1.414214,0.000000,-1.414214,-2.000000,-1.414214,-0.000000,1.414214,2.000000]);\n",
    "# axis centered at (0,0)\n",
    "pyplot.plot(x_1,y_1);\n",
    "pyplot.title(\"Space Profile at t = T/4 for the wave    y= 2*sin(10*pi*t - (pi*x)/40  + pi/4)\")\n",
    "pyplot.xlabel(\"x (in m)\")\n",
    "pyplot.ylabel(\"y1(x)  (in m)\")\n",
    "pyplot.show()\n",
    "#(b)\n",
    "x2= lambd/8.; #in m\n",
    "t2=0; # time period in s\n",
    "print\"The time profile of a wave y= 2*sin(10*pi*t - (pi*x)/40 + pi/4) when  x= lambd/8\\n\\n\"\n",
    "print\"\\t t(in s)     \\t     y2(t) (in m)\\n\\n\"\n",
    "while t2<0.4:\n",
    "\ty2=2*math.sin((omega*t2)-(k*x2)+ (math.pi/4));\n",
    "\tprint \"\\t\",x2,\"\\t\\t\",y2,\"\\n\"\n",
    "\tt2=t2+0.025;\n",
    "\n",
    "#Now,we will plot the time profile from the values obtained for y2 ,for each value of t2\n",
    "x_2=numpy.array([0,0.025,0.05,0.075,0.1,0.125,0.15,0.175,0.2,0.22500,0.250000,0.27500,0.30000,0.325000,0.350000,0.37500])\n",
    "y_2=numpy.array([0.000000,1.414214,2.000000,1.414214,0.000000,-1.414214,-2.000000,-1.414214,-0.000000,1.414214,2.000000,1.414214,0.000000,-1.414214,-2.000000,-1.414214])\n",
    "# axis centered at (0,0)\n",
    "pyplot.plot(x_2,y_2);\n",
    "pyplot.title(\"Time Profile at x = lambd/8 for the wave    y= 2*sin(10*pi*t - (pi*x)/40  + pi/4)\")\n",
    "pyplot.xlabel(\"t (in s)\")\n",
    "pyplot.ylabel(\"y2(t)  (in m)\")\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 3 - pg 33"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Wave parameters from the space profile and time profile\n",
      "\n",
      " (1)Amplitude is (m) =  0.02\n",
      " (2)Wavelength  is (m) =  6\n",
      " (3)Time period is (s) =  2.0\n",
      " (4)Frequency is (Hz) =  0.5\n",
      " (5)Angular Frequency is (rad/s) = 3.14\n",
      " (6)Wave number is (rad/m) =  1.05\n",
      " (7)Initial phase is (radians) =  3.14\n",
      " (8)The velocity of wave is (m/s) =  3.0\n",
      " (9)Intensity is proportional to : 4.0 x 10^-4 m^2.\n"
     ]
    }
   ],
   "source": [
    "#calculate the velocity of wave and Intensity\n",
    "#given\n",
    "import math\n",
    "from math import sin,asin\n",
    "#Let us consider, wave function  y = A*sin(omega*t - K*x + phi)\n",
    "A= 0.02;# Amplitude in m\n",
    "lambd = 6; # Wavelength (lambd) = Crest Distance = 6 m\n",
    "T= 2.;# Time period is s\n",
    "#calculations and results\n",
    "nu =  1/T; # Frequency in Hz\n",
    "omega = 2*math.pi*nu ; #Angular Frequency in rad/s\n",
    "k = 2*math.pi/lambd; #wave number in rad/m\n",
    "#from Space profile, when x=1.5 m, t= 0\n",
    "y = 0.02; #in m\n",
    "x=1.5;#in m\n",
    "t= 0; # in s\n",
    "phi = (asin(y/A) +(k*x) - (omega*t)); # Initial phase in radians\n",
    "print\" Wave parameters from the space profile and time profile\\n\"\n",
    "print\" (1)Amplitude is (m) = \",A\n",
    "print\" (2)Wavelength  is (m) = \",lambd\n",
    "print\" (3)Time period is (s) = \",T\n",
    "print\" (4)Frequency is (Hz) = \",nu\n",
    "print\" (5)Angular Frequency is (rad/s) =\",round(omega,2)\n",
    "print\" (6)Wave number is (rad/m) = \",round(k,2)\n",
    "print\" (7)Initial phase is (radians) = \",round(phi,2)\n",
    "# y(x,t=0) : -0.02 = 0.02*sin(0-(pi*x)/3 + pi)\n",
    "#Thus  (-pi*x)/3 + pi = -pi/2,-5*pi/2, giving x= 9/2 m,21/2m\n",
    "V= omega/k; # Velocity of wave in m/s\n",
    "# I is proportional to A**2\n",
    "I = A**2; # Intensity in m**2 (Proportional)\n",
    "print\" (8)The velocity of wave is (m/s) = \",V\n",
    "print\" (9)Intensity is proportional to :\",I*10**4,\"x 10^-4 m^2.\"\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 6 - pg 39"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For Sound wave :\n",
      "Frequency: (Hz) =  440.0\n",
      "Velocity: (m/s) =  340.0\n",
      "Wavelegth: (m) =  0.773\n",
      "Wave number : (m) = 8.13\n",
      "Wave Equation for Sound wave: y =  A*sin(( 8.13 *x)-( 2764.6 *t)) \n",
      "For Light wave :\n",
      "Frequency:  5.0  x 10^14 Hz\n",
      "Velocity: 3.0  x 10^8 m/s \n",
      "Wavelegth: 6.0  x 10^-7 m\n",
      "Wave number :  1.05 10^7 m\n",
      "Wave Equation for Sound wave: y =  A*sin(( 1.05 *10^7*x)-( 3.14 *10^15*t))\n"
     ]
    }
   ],
   "source": [
    "#calculate the parameters for light and sound waves\n",
    "#(a)Tunning fork \n",
    "#given\n",
    "import math\n",
    "nu= 440.; # Frequency in Hz\n",
    "V=340.; # velocity of sound in air in m/s\n",
    "#calculations\n",
    "lambd= V/nu ;# Wavelength of sound wave in m\n",
    "k= 2*math.pi/lambd; # Wave number in m\n",
    "#(b) Red Light \n",
    "nu1 = 5.*10**14;# Frequency of Red light in Hz\n",
    "V1 = 3.*10**8;#Velocity of light in m/s\n",
    "lambd1= V1/nu1; #Wavelength of light wave in m\n",
    "k1= 2*math.pi/lambd1; # Wave number in m\n",
    "#results\n",
    "print \"For Sound wave :\" \n",
    "print \"Frequency: (Hz) = \",nu\n",
    "print \"Velocity: (m/s) = \",V\n",
    "print \"Wavelegth: (m) = \",round(lambd,3)\n",
    "print \"Wave number : (m) =\",round(k,2)\n",
    "print \"Wave Equation for Sound wave: y =  A*sin((\",round(k,2),\"*x)-(\",round((2*math.pi*nu),2),\"*t)) \"\n",
    "print \"For Light wave :\"\n",
    "print \"Frequency: \",nu1*10**-14,\" x 10^14 Hz\" \n",
    "print \"Velocity:\",V1*10**-8,\" x 10^8 m/s \"\n",
    "print \"Wavelegth:\",lambd1*10**7,\" x 10^-7 m\"\n",
    "print \"Wave number : \",round(k1*10**-7,2),\"10^7 m\"\n",
    "print \"Wave Equation for Sound wave: y =  A*sin((\",round(k1*10**-7,2),\"*10^7*x)-(\",round(2*math.pi*nu1*10**-15,2),\"*10^15*t))\""
   ]
  }
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