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diff --git a/Oscillations_and_Waves_by_S._Prakash/chapter8.ipynb b/Oscillations_and_Waves_by_S._Prakash/chapter8.ipynb new file mode 100755 index 00000000..eb4bafc3 --- /dev/null +++ b/Oscillations_and_Waves_by_S._Prakash/chapter8.ipynb @@ -0,0 +1,563 @@ +{ + "metadata": { + "name": "", + "signature": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "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": {} + } + ] +} |