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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 5, Wave motion and speed of waves in gases"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1, page 206"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "# wavelength\n",
      "#given data :\n",
      "v=960 # in m/s\n",
      "n=3600/60 # in per sec\n",
      "lamda=v/n \n",
      "print \"The wavelength, lamda = %0.f m \" %lamda"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The wavelength, lamda = 16 m \n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 2, page 206"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Frequency\n",
      "#given data :\n",
      "c=3*10**8 # in m/s\n",
      "lamda=300 # in m\n",
      "n=c*10**-6/lamda \n",
      "print \"The frequency, n = %0.f MHz \" %n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The frequency, n = 1 MHz \n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3, page 208"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# velocity and direction\n",
      "#y=1.2*sin(3.5*t+0.5*x) #equation\n",
      "w=3.5 #from equation\n",
      "k=0.5 #from equation\n",
      "v=w/k #m/s\n",
      "print \"wave velocity =\",v,\"m/s and direction of the wave is along negative X-axis\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "wave velocity = 7.0 m/s and direction of the wave is along negative X-axis\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 4, page 209"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sympy import symbols, pi, sin\n",
      "#equation of wave propogation\n",
      "amp=0.02 #m\n",
      "fr=110 #Hz\n",
      "v=330 #m/s\n",
      "w=2*pi*fr #s**-1\n",
      "k=w/v #constant\n",
      "t, x = symbols('t x')\n",
      "y=amp*sin(w*t-k*x) #refrence equation\n",
      "print \"Equation of wave is\",y"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Equation of wave is 0.02*sin(220*pi*t - 2*pi*x/3)\n"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 5, page 211"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from numpy import pi\n",
      "#path difference\n",
      "v=360 #m/s\n",
      "fr=500 #Hz\n",
      "h=v/fr #wavelength in metre\n",
      "ang=60 #degree\n",
      "angr=ang*(pi/180) #radian\n",
      "pth=(h)/(2*pi) #metre\n",
      "print \"Path difference = %0.2f m \" %pth"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Path difference = 0.11 m \n"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6, page 211"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from math import pi\n",
      "#path difference\n",
      "pth=15 #cm\n",
      "pd=(2*pi)/3 #radians\n",
      "h=(pth*2*pi)/pd #cm\n",
      "print \"Wavelength = %0.f cm \" %h"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Wavelength = 45 cm \n"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 8, page 214"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from math import sin,degrees\n",
      "from sympy import pi\n",
      "#displacement ,particle velocity and acceleration\n",
      "x=200 #cm\n",
      "a=3 # cm\n",
      "v=1000#cm/s\n",
      "n=25\n",
      "lamda=v/n \n",
      "y=a*sin(2*pi/lamda*(v*t-x))\n",
      "\n",
      "v=1000 #cm/s\n",
      "n=25 #vibrations\n",
      "h=v/n #cm\n",
      "a=3 #cm\n",
      "t=2 #seconds\n",
      "vl=2*pi*a*n #cm/s\n",
      "acc=0 #\n",
      "print \"Displacement c = %0.f m \" %round(abs(y))\n",
      "print \"Velocity =\",vl,\"cm/s \" \n",
      "print \"Acceleration = %0.2f cm/s^2 \" %acc"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Displacement c = 0 m \n",
        "Velocity = 150*pi cm/s \n",
        "Acceleration = 0.00 cm/s^2 \n"
       ]
      }
     ],
     "prompt_number": 62
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 9, page 215"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#amplitude,frequency,velocity ,wavelength and speed\n",
      "#y=5*sin*(4t-0.02x) #given\n",
      "a=5 #cm \n",
      "h=(2*pi)/0.02 #\n",
      "v=0.02*10000 #cm/s\n",
      "n=v/h #cycles/seconds\n",
      "print \"Amplitude = %0.2f cm \" %a\n",
      "print \"Frequency = %0.3f cycles/s \" %n\n",
      "print \"Velocity = %0.f cm/s \" %v\n",
      "print \"Wavelength = %0.f cm \" %h\n",
      "ma1x=a*4 #cm/s\n",
      "print \"Maximum speed = %0.2f cm/s \" %ma1x"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Amplitude = 5.00 cm \n",
        "Frequency = 0.637 cycles/s \n",
        "Velocity = 200 cm/s \n",
        "Wavelength = 314 cm \n",
        "Maximum speed = 20.00 cm/s \n"
       ]
      }
     ],
     "prompt_number": 66
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 10, page 216"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from math import pi\n",
      "#wave intensity\n",
      "nt=1 #watt source\n",
      "r=1 #n\n",
      "Is=(nt/(4*pi*r**2)) # joule/sec-m**2\n",
      "print \"Intensity on the surface = %0.2f J/s-m^2 \" %Is"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Intensity on the surface = 0.08 J/s-m^2 \n"
       ]
      }
     ],
     "prompt_number": 67
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 14, page 225"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Energy flux \n",
      "#given data :\n",
      "A=.10 # in m\n",
      "w=4 # in per sec\n",
      "k=0.1 # in per cm\n",
      "p=1.25*10**3 # in kg/m**3\n",
      "v=w*10**-2/k # in m/s\n",
      "n=w/(2*pi) \n",
      "Ef=2*pi**2*n**2*A**2*p*v \n",
      "print \"Energy flux of the wave, Ef = %0.f W/m^2 \" %Ef"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Energy flux of the wave, Ef = 40 W/m^2 \n"
       ]
      }
     ],
     "prompt_number": 69
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 15, page 225"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Energy radiated and energy current\n",
      "#given data :\n",
      "p=1.29 # in kg/m**3\n",
      "a=.15*10**-2 # in m/s\n",
      "n=76 # in Hz\n",
      "E=2*pi**2*n**2*a**2*p \n",
      "print \"(a) Energy radiated, E = %0.3f J/m^3 \" %E\n",
      "v=332 # in m/s\n",
      "Ev=E*v \n",
      "print \"(b) The energy current, Ev = %0.2f W/s \" %Ev\n",
      "# energy current is calculated wrong in the textbook"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(a) Energy radiated, E = 0.331 J/m^3 \n",
        "(b) The energy current, Ev = 109.87 W/s \n"
       ]
      }
     ],
     "prompt_number": 71
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 16, page 234"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Pressure amplitude, Energy density and energy flux\n",
      "#given data :\n",
      "a=10**-5 # in m\n",
      "n=500 # in per sec\n",
      "p=1.29 # in kg/m**3\n",
      "v=340 # in m/s\n",
      "Pa=2*pi*a*n*v*p \n",
      "print \"(i) Pressure amplitude, Pa = %0.1f N/m^2 \" %Pa\n",
      "Ed=2*pi**2*a**2*n**2*p \n",
      "print \"(ii) Energy density, Ed = %0.1e J/m^3 \"%Ed\n",
      "Ef=2*pi**2*a**2*n**2*p*v \n",
      "print \"(iii) The energy flux, Ef = %0.2f J/m^2-s \" %Ef"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(i) Pressure amplitude, Pa = 13.8 N/m^2 \n",
        "(ii) Energy density, Ed = 6.4e-04 J/m^3 \n",
        "(iii) The energy flux, Ef = 0.22 J/m^2-s \n"
       ]
      }
     ],
     "prompt_number": 74
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 17, page 235"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Pressure \n",
      "#given data :\n",
      "gama=1.4 \n",
      "u=10**-3 # in m/s\n",
      "v=340 # in m/s\n",
      "P=10**5 # in N/m**2\n",
      "p=gama*P*u/v \n",
      "print \"The pressure, p = %0.2f N/m^2  \" %p"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The pressure, p = 0.41 N/m^2  \n"
       ]
      }
     ],
     "prompt_number": 77
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 18, page 238"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from math import sqrt\n",
      "#speed\n",
      "sa=332 #m/s\n",
      "pa=16 #density of air\n",
      "ph=1 #density of hydrogen\n",
      "vn=sa*sqrt(pa/ph) #m/s\n",
      "t1=0 #degree celsius\n",
      "t2=546 #degree celsius\n",
      "t1k=0+273 #kelvin\n",
      "t2k=t2+273 #kelvin\n",
      "v2=vn*sqrt(t2k/t1k) #m/s\n",
      "print \"Speed of sound in first case = %0.f m/s \" %vn\n",
      "print \"speed of sound in second case is = %0.f m/s\" %v2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Speed of sound in first case = 1328 m/s \n",
        "speed of sound in second case is = 2300 m/s\n"
       ]
      }
     ],
     "prompt_number": 80
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 19, page 239"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#temperature\n",
      "t1=0 #degree celsius\n",
      "t1k=t1+273 #kelvin\n",
      "rt=2 #\n",
      "tk=rt**2*t1k #Kelvin\n",
      "t=tk-273 #degree celsius\n",
      "print \"Temperature = %0.f degree-celsius \" %t"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Temperature = 819 degree-celsius \n"
       ]
      }
     ],
     "prompt_number": 81
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 20, page 239"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#temperature\n",
      "rtd=16/14 #ratio of densities\n",
      "tk=15+273 #degree celsius\n",
      "x=(tk*rtd)-273 #degree celsius\n",
      "print \"Temperature = %0.2f degree-celsius \" %x"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Temperature = 56.14 degree-celsius \n"
       ]
      }
     ],
     "prompt_number": 82
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 21, page 240"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#speed\n",
      "rt=4/1 #\n",
      "ss=332 #m/s\n",
      "rd=32/28 #ratio of densities\n",
      "rt1=((1+(1/rt)*rd)/(1+(1/rt))) #\n",
      "v1=ss*sqrt(rt1) #m/s\n",
      "print \"Speed of sound in nitrogen = %0.1f m/s \" %v1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Speed of sound in nitrogen = 336.7 m/s \n"
       ]
      }
     ],
     "prompt_number": 84
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 22, page 241"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#speed\n",
      "gm=1.41 #\n",
      "vs=330 #m/s\n",
      "vrms=sqrt(3/gm)*vs #m/s\n",
      "print \"Root mean square velocity of molecules of gas = %0.f m/s \" %vrms"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Root mean square velocity of molecules of gas = 481 m/s \n"
       ]
      }
     ],
     "prompt_number": 86
    }
   ],
   "metadata": {}
  }
 ]
}