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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 8, Vibrations of strings & membranes"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 1, page 317"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "from numpy import sqrt\n",
      "# Speed\n",
      "#given data :\n",
      "m1=0.1 # in kg\n",
      "g=9.81 # in m/s**2\n",
      "T=m1*g # N\n",
      "A=10**-6 # in m**2\n",
      "p=9.81*10**3 # in kg/m**3\n",
      "m=A*p # in kg/m\n",
      "v=sqrt(T/m) \n",
      "print \"The speed of transverse waves, v = %0.f m/s  \" %v"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The speed of transverse waves, v = 10 m/s  \n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 2, page 318"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# tensile stress\n",
      "#given data :\n",
      "p=8000 # in kg/m**3\n",
      "v=340 # in m/s\n",
      "TbyA=v**2*p*10**-2 \n",
      "print \"Tensile stress = %0.2e N/m^2  \" %TbyA"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Tensile stress = 9.25e+06 N/m^2  \n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3, page 323"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Tension\n",
      "#given data :\n",
      "M=2*10**-3 # in kg\n",
      "l=35*10**-2 # in m\n",
      "n=500 # in Hz\n",
      "m=M/l # in kg/m\n",
      "T=4*n**2*l**2*m \n",
      "print \"Tension, T = %0.f N  \" %T"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Tension, T = 700 N  \n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 4, page 324"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Frequency\n",
      "#given data :\n",
      "T=625 # in N\n",
      "T1=100 # in N\n",
      "l=1/2 \n",
      "n=240 # in Hz\n",
      "n1=1/l*(sqrt(T1/T))*n \n",
      "print \"The frequency, n1 = %0.f Hz \" %n1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The frequency, n1 = 192 Hz \n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 5, page 324"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# initial tension\n",
      "rt=2/3 #ratio\n",
      "mi=5 #kg wt\n",
      "M=((1/rt)**2)-1 #\n",
      "mo=mi/M #kg wt\n",
      "print \"Initial tension in string = %0.2f kg-wt  \" % mo"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Initial tension in string = 4.00 kg-wt  \n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6, page 325"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# speed,stress and change in frequency\n",
      "n=175 #Hz\n",
      "l=1.5 #m\n",
      "v=2*n*l #m/s\n",
      "d=7.8*10**3 #kg/m**3\n",
      "st=v**2*d #N/m**2\n",
      "per=3 #% increament\n",
      "T=1 #assume\n",
      "td=(1+per/100)*T #\n",
      "x=(((1/2)*(per/100))) #\n",
      "td=x*100 #\n",
      "print \"Velocity = %0.2f m/s \" % v\n",
      "print \"Stress = %0.2e N/m^2 \" %st\n",
      "print \"Percentage change in frequency = %0.1f %% \" %td"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Velocity = 525.00 m/s \n",
        "Stress = 2.15e+09 N/m^2 \n",
        "Percentage change in frequency = 1.5 % \n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7, page 326"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Frequency\n",
      "#given data :\n",
      "l=.50 # in m\n",
      "m1=25 # in kg\n",
      "m2=1.44*10**-3 # in kg\n",
      "g=9.81 # in m/s**2\n",
      "T=m1*g \n",
      "m=m2/l \n",
      "p=2 \n",
      "n=(p/(2*l))*sqrt(T/m) \n",
      "print \"The frequency, n = %0.1f \" %n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The frequency, n = 583.6 \n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 8, page 326"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# frequency\n",
      "l1=90 #cm\n",
      "d1=0.05 #cm\n",
      "d2=0.0625 #cm\n",
      "l2=60 #cm\n",
      "n1=200 #Hz\n",
      "n2=((l1*d1*n1)/(l2*d2)) #Hz\n",
      "print \"Frequency = %0.2f Hz  \" % n2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Frequency = 240.00 Hz  \n"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 9, page 327"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# tension\n",
      "n21=3/2 #\n",
      "r21=3/4 #\n",
      "t1=2.048 #kg. wt\n",
      "t2=(n21*r21)**2*t1 #kg weight\n",
      "n31=9/4 #\n",
      "r31=2/4 #\n",
      "t3=(n31*r31)**2*t1 #kg-weight\n",
      "n41=27/8 #\n",
      "r41=1/4 #\n",
      "t4=(n41*r41)**2*t1 #kg-weight\n",
      "print \"Tension, T2 = %0.3f kg weight\"%t2\n",
      "print \"Tension, T3 = %0.3f kg weight\"%t3\n",
      "print \"Tension, T4 = %0.3f kg weight\"%t4"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Tension, T2 = 2.592 kg weight\n",
        "Tension, T3 = 2.592 kg weight\n",
        "Tension, T4 = 1.458 kg weight\n"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 10, page 328"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from math import sqrt\n",
      "# velocity\n",
      "l1=20 #cm\n",
      "v1=600 #cm**-1\n",
      "n1=v1/4 #\n",
      "v1=2*n1*l1*10**-2 #m/sec\n",
      "v2=sqrt(2)*v1 #m/s\n",
      "print \"Velocity of the waves = %0.f m/s \" %v1\n",
      "print \"Velocity of waves when tension of the string is doubled = %.f m/s \" %round(v2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Velocity of the waves = 60 m/s \n",
        "Velocity of waves when tension of the string is doubled = 85 m/s \n"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 11, page 331"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# frequency\n",
      "nb=6 #beats\n",
      "l1=20 #cm\n",
      "l2=21 #cm\n",
      "x=l2/l1 #\n",
      "n=(x*nb+nb)/(x-1) #\n",
      "print \"Frequency = %0.f Hz \" %n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Frequency = 246 Hz \n"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 12, page 331"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# frequency\n",
      "nb=4 #beats\n",
      "l1=70 #cm\n",
      "l2=70-1 #cm\n",
      "x=l2/l1 #\n",
      "n=(x*nb)/(1-x) #\n",
      "print \"Frequency = %0.f Hz \" %n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Frequency = 276 Hz \n"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 13, page 332"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# length\n",
      "n123=1/3/15 #\n",
      "tl=105 #cm\n",
      "l123=15/5/1 #\n",
      "k=tl/21 #\n",
      "l1=15*k #cm\n",
      "l2=5*k #cm\n",
      "l3=k #cm\n",
      "print \"l1 length = %0.f cm\"%l1\n",
      "print \"l2 length = %0.f cm\"%l2\n",
      "print \"l3 length = %0.f cm\"%l3\n",
      "#length l2 is calculated wrong in the textbook"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "l1 length = 75 cm\n",
        "l2 length = 25 cm\n",
        "l3 length = 5 cm\n"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 15, page 355"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from math import sqrt\n",
      "# frequency\n",
      "l=2.5 #m\n",
      "m1=0.001 #kg\n",
      "tn=4 #N\n",
      "m=m1/l #kg/m\n",
      "n=((1/(2*l))*sqrt(tn/m)) #Hz\n",
      "print \"Frequency = %0.2f Hz \" %n\n",
      "print \"Frequencies stopped are\",5*n,\"Hz, \",10*n,\"Hz, \",15*n,\"Hz\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Frequency = 20.00 Hz \n",
        "Frequencies stopped are 100.0 Hz,  200.0 Hz,  300.0 Hz\n"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 16, page 356"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from math import pi\n",
      "# frequency\n",
      "l=1 #m\n",
      "m1=0.5 #kg\n",
      "tn=200 #N\n",
      "m=m1/l #kg/m\n",
      "n=((1/(2*l))*sqrt(tn/m)) #Hz\n",
      "print \"Frequency = %0.2f Hz \" %n\n",
      "w=2*pi*n #\n",
      "print \"Ratio of three frequencies is %0.1f:%0.1f:%0.1f\"%(w,2*w,3*w)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Frequency = 10.00 Hz \n",
        "Ratio of three frequencies is 62.8:125.7:188.5\n"
       ]
      }
     ],
     "prompt_number": 25
    }
   ],
   "metadata": {}
  }
 ]
}