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| author | Thomas Stephen Lee | 2015-08-28 16:53:23 +0530 |
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| committer | Thomas Stephen Lee | 2015-08-28 16:53:23 +0530 |
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| tree | 31b43ae8895599f2d13cf19395d84164463615d9 /Oscillations_and_Waves_by_S._Prakash | |
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diff --git a/Oscillations_and_Waves_by_S._Prakash/README.txt b/Oscillations_and_Waves_by_S._Prakash/README.txt new file mode 100644 index 00000000..f20b94b1 --- /dev/null +++ b/Oscillations_and_Waves_by_S._Prakash/README.txt @@ -0,0 +1,10 @@ +Contributed By: Mohd Asif +Course: btech +College/Institute/Organization: Pentode Technologies +Department/Designation: Technical Executive +Book Title: Oscillations and Waves +Author: S. Prakash +Publisher: Pragati Prakashan, Merut +Year of publication: 2008 +Isbn: 978-81-8398-422-5 +Edition: 5
\ No newline at end of file diff --git a/Oscillations_and_Waves_by_S._Prakash/chapter1.ipynb b/Oscillations_and_Waves_by_S._Prakash/chapter1.ipynb new file mode 100755 index 00000000..9c8321a9 --- /dev/null +++ b/Oscillations_and_Waves_by_S._Prakash/chapter1.ipynb @@ -0,0 +1,849 @@ +{ + "metadata": { + "name": "", + "signature": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter1 - Free oscillations in one-dimension : Simple harmonic Oscillator" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1, page 9" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from __future__ import division\n", + "from math import sqrt, pi\n", + "# FREQUENCY AND TIME PERIOD\n", + "#format('v',6)\n", + "#ph=50*x**2+100 in joule/kg\n", + "m=10 #mass in kg\n", + "f=10**3/m #joule/kg\n", + "w=sqrt(f) #oscillations\n", + "fr=w/(2*pi) #oscillations/sec\n", + "tp=1/fr #seconds\n", + "print \"Frequency of oscillation = %0.1f oscillations/seconds \"%fr\n", + "print \"Time period = %0.3f seconds \" %tp" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Frequency of oscillation = 1.6 oscillations/seconds \n", + "Time period = 0.628 seconds \n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3, page 11" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# ENERGY\n", + "ke=5 #joule\n", + "pe=5 #joule\n", + "rep=10 #joule\n", + "eo=rep+ke+pe #joule\n", + "print \"Energy of the oscillator = %0.f J\" %eo" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Energy of the oscillator = 20 J\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4, page 12" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#peroid ,maximum velocity and acceleration\n", + "a=3 #cm\n", + "b=4 #cm\n", + "A=sqrt(a**2+b**2) #cm\n", + "w=2 #sec**-1\n", + "T=(2*pi)/w #seconds\n", + "um=w*A #cm/s\n", + "am=w**2*A #cm/s**2\n", + "print \"Time period = %0.f seconds\" %T\n", + "print \"Maximum velocity = %0.f cm/s\" %um\n", + "print \"Maximum acceleration = %0.f cm/s2 \" %am" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Time period = 3 seconds\n", + "Maximum velocity = 10 cm/s\n", + "Maximum acceleration = 20 cm/s2 \n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5, page 12" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi\n", + "# maximum velocity and acceleration\n", + "A=5 #cm\n", + "T=31.4#seconds\n", + "w=(2*pi)/T #sec**-1\n", + "um=w*A #cm/s\n", + "am=w**2*A #cm/s**2\n", + "print \"Maximum velocity = %0.f cm/s\" %um\n", + "print \"Maximum acceleration = %0.1f cm/s2 \" %am" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Maximum velocity = 1 cm/s\n", + "Maximum acceleration = 0.2 cm/s2 \n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6, page 20" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi, sqrt\n", + "# Period \n", + "#given data :\n", + "g=9.8 # constant\n", + "l=1 # in m\n", + "theta_m1=60 # in degree\n", + "theta_m=pi/3 # in radians\n", + "T0=round(2*pi*sqrt(l/g)) \n", + "print \"(a) Time period for small displacement, T0 = %0.f seconds \" %T0\n", + "T=T0*(1+(theta_m**2/16)) \n", + "print \"(b) Time period, T = %0.1f seconds \" %T" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(a) Time period for small displacement, T0 = 2 seconds \n", + "(b) Time period, T = 2.1 seconds \n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7, page 20" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# ENERGY\n", + "es=1 #joule\n", + "l=2 #metre\n", + "am=3 #cm\n", + "am1=5 #cm\n", + "e1=(am1**2/am**2)*es #joules\n", + "l2=1 #meter\n", + "e2=(l/l2)*es #joules\n", + "print \"Energy in first case = %0.3f J\" %e1\n", + "print \"Energy in second case = %0.1f J\" %e2" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Energy in first case = 2.778 J\n", + "Energy in second case = 2.0 J\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8, page 28" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt, pi\n", + "# Period of motion\n", + "#given data :\n", + "x=0.16 # in m\n", + "m1=4 # in kg\n", + "g=9.8 \n", + "K=m1*g/x \n", + "m=0.50 # in kg\n", + "T=2*pi*sqrt(m/K) # \n", + "print \"The period of motion, T = %0.2f seconds \" %T\n", + "# answer is wrong in textbook" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The period of motion, T = 0.28 seconds \n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9, page 28" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt\n", + "#foce constant,displacement , acceleration and energy\n", + "#given data :\n", + "x1=.10 # in m\n", + "F1=4 # in N\n", + "K=F1/x1 \n", + "x2=0.12 # in m\n", + "print \"(a) The force constant, K = %0.2f N/m\" %K\n", + "F=-K*x2 \n", + "print \"(b) The force, F = %0.2f N\" %F\n", + "m=1.6 # in kg\n", + "T=2*pi*sqrt(m/K) \n", + "print \"(c) Period of oscillation, T = %0.3f s \" %T\n", + "A=x2 \n", + "print \"(d) Amplitude of motion, A = %0.2f m \" %A\n", + "alfa=A*K/m \n", + "print \"(e) Maximum acceleration, alfa = %0.2f m/s2 \" %alfa\n", + "x=A/2 # in m\n", + "w=sqrt(K/m) \n", + "v=w*sqrt(A**2-x**2) \n", + "a=w**2*x # in m/s**2\n", + "KE=(1/2)*m*v**2 # in J\n", + "PE=(1/2)*K*x**2 # in J\n", + "TE=KE+PE \n", + "print \"(f) Velocity = %0.2f m/s \" %v\n", + "print \"(f) Acceleration = %0.2f m/s2 \" %a\n", + "print \"(f) Kinetic energy = %0.2f J \" %KE\n", + "print \"(f) Potential energy = %0.2f J\" %PE\n", + "print \"(g) Total energy of the oscillating system, TE = %0.2f J\" %TE\n", + "# In textbook part f is inculded in the part e so their is the numbeing error in parts" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(a) The force constant, K = 40.00 N/m\n", + "(b) The force, F = -4.80 N\n", + "(c) Period of oscillation, T = 1.257 s \n", + "(d) Amplitude of motion, A = 0.12 m \n", + "(e) Maximum acceleration, alfa = 3.00 m/s2 \n", + "(f) Velocity = 0.52 m/s \n", + "(f) Acceleration = 1.50 m/s2 \n", + "(f) Kinetic energy = 0.22 J \n", + "(f) Potential energy = 0.07 J\n", + "(g) Total energy of the oscillating system, TE = 0.29 J\n" + ] + } + ], + "prompt_number": 20 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10, page 30" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sin\n", + "from sympy import symbols, pi\n", + "# ENERGY\n", + "t=8/3 #seconds\n", + "v=-10*pi*sin((35*pi)/6)#cm/s\n", + "print \"Velocity =\",v,\"cm\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Velocity = 5.0*pi cm\n" + ] + } + ], + "prompt_number": 31 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11, page 30" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt, pi\n", + "#given data :\n", + "K1=3 # in N/m\n", + "K2=2 # in N/m\n", + "m=0.050 # in kg\n", + "w=sqrt((K1+K2)/m) \n", + "n=w/(2*pi) \n", + "print \"(i) The frequency, n = %0.2f oscillations/sec \" %n\n", + "A=0.004 # in m\n", + "E=(1/2)*A**2*(K1+K2) \n", + "print \"(ii) The energy, E = %0.e J \" %E\n", + "v=sqrt(2*E/m) \n", + "print \"(iii) The velocity, v = %0.2f m/s\" %v" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(i) The frequency, n = 1.59 oscillations/sec \n", + "(ii) The energy, E = 4e-05 J \n", + "(iii) The velocity, v = 0.04 m/s\n" + ] + } + ], + "prompt_number": 35 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12, page 33" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Rotational inertia\n", + "#given data :\n", + "M=0.1 # in m\n", + "l=0.1 # in m\n", + "I1=M*l**2/12 # in kg-m**2\n", + "T1=2 # in s\n", + "T2=6 # in s\n", + "I2=(I1*T2**2)/T1**2 \n", + "print \"Rotational inertia, I2 = %0.1e kg-m2 \" %I2" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Rotational inertia, I2 = 7.5e-04 kg-m2 \n" + ] + } + ], + "prompt_number": 38 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13, page 34" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt\n", + "# Time period\n", + "#given data :\n", + "M=4 # in kg\n", + "R=0.10 # in m\n", + "I=(2/5)*M*R**2 # in kg.m**2\n", + "C=4*10**-3 # in Nm/radian\n", + "T=2*pi*sqrt(I/C) \n", + "print \"Time period, T = %0.2f s \" %T\n", + "# answer is wrong in textbook" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Time period, T = 12.57 s \n" + ] + } + ], + "prompt_number": 39 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 15, page 41" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt, pi\n", + "# Energy\n", + "#given data :\n", + "L=10*10**-3 # in H\n", + "C=20*10**-6 # in F\n", + "n=1/(2*pi*sqrt(L*C)) \n", + "V=10 #in V\n", + "U=(1/2)*C*V**2 \n", + "print \"Frequency, n = %0.2f cycles/s \" %n\n", + "print \"Energy of oscillations,U = %0.1e J \" %U\n", + "#answer of frequency is calculated wrong in textbook" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Frequency, n = 355.88 cycles/s \n", + "Energy of oscillations,U = 1.0e-03 J \n" + ] + } + ], + "prompt_number": 41 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 16, page 47" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# distance,binding energy and force constant\n", + "print \"Equilibrium inter-nuclear distance correspondes to lowest potential enegy is ro= 2*\u00c5\"\n", + "pet=0 #eV\n", + "peb=-4 #eV\n", + "be=pet-peb #eV\n", + "x1=-2 #eV\n", + "x2=-4 #eV\n", + "V=x1-x2 #eV\n", + "e=1.6*10**-19 #electronic charge\n", + "x=0.5 #armstrong\n", + "K=((2*V)/x**2) #eV/\u00c5**2\n", + "k1=(K*e)/(10**-10)**2 #joule/m**2\n", + "print \"Binding energy = %0.2f eV \" %be\n", + "print \"Force constant = %0.2f N/m \" %k1" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Equilibrium inter-nuclear distance correspondes to lowest potential enegy is ro= 2*\u00c5\n", + "Binding energy = 4.00 eV \n", + "Force constant = 256.00 N/m \n" + ] + } + ], + "prompt_number": 42 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 17, page 48" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# possible values and energy\n", + "r1=2 #from graph\n", + "r2=4.5 #units from graph\n", + "print \"Possible values of r are\",r1,\"units and\",r2,\"units.\"\n", + "osc=1-(-2.5) #units\n", + "print \"Maximum energy of oscillations for r=2 units is\",osc,\"units.\"\n", + "osc1=0.5-(-1) #units\n", + "print \"Maximum energy of oscillations for r=4.5 units is\",osc1,\"units.\"\n", + "t=1 #from graph\n", + "v=0 #from graph\n", + "e=t+v #\n", + "print \"Total energy = %0.2f unit \" %e\n", + "print \"At infinity V =\",v,\"therefore T =\",t,\"unit.\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Possible values of r are 2 units and 4.5 units.\n", + "Maximum energy of oscillations for r=2 units is 3.5 units.\n", + "Maximum energy of oscillations for r=4.5 units is 1.5 units.\n", + "Total energy = 1.00 unit \n", + "At infinity V = 0 therefore T = 1 unit.\n" + ] + } + ], + "prompt_number": 43 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 19, page 67" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt, pi\n", + "# Frequency\n", + "#given data :\n", + "m1=10 # in g\n", + "m2=90 # in g\n", + "K=10**3 # in N/m\n", + "mu=m1*m2*10**-3/(m1+m2) \n", + "n=round(sqrt(K/mu)/(2*pi)) \n", + "print \"The frequency, n = %0.2f oscillations/sec \" %n\n", + "x1=0 #\n", + "x2=10 #cm\n", + "xb=((m1*x1+m2*x2)/(m1+m2)) #cm\n", + "mo=(m1*10**-3)*(xb*10**-2)**2+(m2*10**-3)*(1*10**-2)**2 #\n", + "print \"Moment of inertia = %0.1e kg-m2 \" %mo" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The frequency, n = 53.00 oscillations/sec \n", + "Moment of inertia = 9.0e-05 kg-m2 \n" + ] + } + ], + "prompt_number": 45 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 20, page 68" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt, pi\n", + "# frequency and amplitude\n", + "c=10**-4 #N-m\n", + "m1=9 #gm\n", + "m2=1 #gm\n", + "mu=((m1*m2)/(m1+m2))*10**-3 #kg\n", + "r=20 #cm\n", + "I=mu*(r*10**-2)**2 #kg-m**2\n", + "fr=((1/(2*pi))*sqrt(c/I)) #vibrations/sec\n", + "print \"Frequency of vibration = %0.2f vibrations/s \" %fr\n", + "e=10**-2 #joule\n", + "thmax=sqrt((2*e)/c) #radians\n", + "print \"Amplitude = %0.2f radians \" %thmax" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Frequency of vibration = 0.27 vibrations/s \n", + "Amplitude = 14.14 radians \n" + ] + } + ], + "prompt_number": 46 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 21, page 69" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt\n", + "# frequency ,energy and maximum velocity\n", + "c=1 #N-m \n", + "m1=6 #gm\n", + "m2=2 #gm\n", + "mu=((m1*m2)/(m1+m2))*10**-3 #kg\n", + "fr=((1/(2*pi))*sqrt(c/mu)) #vibrations/sec\n", + "print \"Frequency of oscillations = %0.1f vibrations/s \" %fr\n", + "td= 1+(1/3) #cm\n", + "e=((1/2)*c*(td*10**-2)**2) #joule\n", + "print \"Energy = %0.1e J \" %e\n", + "y=((1/2)*m2*10**-3)+((1/2)*(1/3)**2*m1*10**-3) #\n", + "v1=sqrt((e/y)) #m/sec\n", + "print \"Maximum velocity of smaller mass = %0.2f m/s\" %v1\n", + "#velocity is calculated wrong in the book" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Frequency of oscillations = 4.1 vibrations/s \n", + "Energy = 8.9e-05 J \n", + "Maximum velocity of smaller mass = 0.26 m/s\n" + ] + } + ], + "prompt_number": 48 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 22, page 70" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt, pi\n", + "# frequency\n", + "k=100 #N/m\n", + "m=100 #gm\n", + "n1=((1/(2*pi))*sqrt(k/(m*10**-3))) #sec**-1\n", + "m1=100 #gm\n", + "m2=200 #gm\n", + "mu=((m1*m2)/(m1+m2))*10**-3 #kg\n", + "fr=((1/(2*pi))*sqrt(k/mu)) #sec**-1\n", + "print \"In first case frequency = %0.f sec^-1 \"%n1\n", + "print \"In second case frequency = %0.1f sec^-1 \"%fr" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "In first case frequency = 5 sec^-1 \n", + "In second case frequency = 6.2 sec^-1 \n" + ] + } + ], + "prompt_number": 50 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 23, page 73" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# force constant and work done\n", + "m1=1 #assume\n", + "m2=19 #assume\n", + "mh=1.66*10**-27 #kg\n", + "mu=((m1*m2)/(m1+m2))*mh #kg\n", + "w=7.55*10**14 #radians/sec\n", + "k=mu*(w)**2 #N/m\n", + "print \"Force constant = %0.1f N/m \" %k\n", + "x=0.5 #arngstrom\n", + "wh=((1/2)*k*(x*10**-10)**2) #joule\n", + "print \"Work done = %0.3e J\" %wh" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Force constant = 898.9 N/m \n", + "Work done = 1.124e-18 J\n" + ] + } + ], + "prompt_number": 52 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 24, page 74" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt\n", + "# frequency\n", + "m1=1 #a.m.u\n", + "m2=35 #a.m.u\n", + "mu1=((m1*m2)/(m1+m2)) #a.m.u\n", + "m3=2 #\n", + "mu2=((m3*m2)/(m3+m2)) #a.m.u\n", + "n1=8.99*10**13 #cycle/sec\n", + "n2=(sqrt(mu1/mu2))*n1 #c/s\n", + "print \"Frequecy of vibrations = %0.2e c/s \" %n2" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Frequecy of vibrations = 6.44e+13 c/s \n" + ] + } + ], + "prompt_number": 53 + } + ], + "metadata": {} + } + ] +} diff --git a/Oscillations_and_Waves_by_S._Prakash/chapter10.ipynb b/Oscillations_and_Waves_by_S._Prakash/chapter10.ipynb new file mode 100755 index 00000000..9089cf29 --- /dev/null +++ b/Oscillations_and_Waves_by_S._Prakash/chapter10.ipynb @@ -0,0 +1,417 @@ +{ + "metadata": { + "name": "", + "signature": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 10, Waves in solids" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1, page 406" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from __future__ import division\n", + "# Young's modulus of steel\n", + "#given data :\n", + "p=7.8*10**3 # in kg/m**3\n", + "v=5200 # m/s\n", + "Y=p*v**2 \n", + "print \"Young modulus of steel, Y = %0.1e N/m^2 \" %Y" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Young modulus of steel, Y = 2.1e+11 N/m^2 \n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2, page 406" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt\n", + "# Velocity and wavelength\n", + "#given data :\n", + "Y=8*10**10 # in N/m**2\n", + "p=5000 # in kg/m**3\n", + "v=sqrt(Y/p) \n", + "print \"(1) The velocity, v = %0.f m/s \" %v\n", + "f=400 # in vibration/sec\n", + "lamda=v/f \n", + "print \"(2) The wavelength = %0.f m \" %lamda" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(1) The velocity, v = 4000 m/s \n", + "(2) The wavelength = 10 m \n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3, page 406" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Velocity and wavelength\n", + "#given data :\n", + "Y=7*10**10 # in N/m**2\n", + "p=2.8*10**3 # in kg/m**3\n", + "v=sqrt(Y/p) \n", + "print \"(1) The velocity, v = %0.e m/s \" %v\n", + "f=500 # in vibration/sec\n", + "lamda=v/f \n", + "print \"(2) The wavelength = %0.f m \" %lamda" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(1) The velocity, v = 5e+03 m/s \n", + "(2) The wavelength = 10 m \n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4, page 410" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Young's modulus\n", + "#given data :\n", + "l=3 # in m\n", + "n=600 # in Hz\n", + "p=8.3*10**3 # in kg/m**3\n", + "Y=p*n**2*(2*l)**2 \n", + "print \"Youngs modulus, Y = %0.3e N/m^2 \" %Y" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Youngs modulus, Y = 1.076e+11 N/m^2 \n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5, page 411" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Frequency\n", + "#given data :\n", + "Y=2*10**11 # in N/m**2\n", + "p=8*10**3 # in kg/m**3\n", + "l=0.25 # in m\n", + "n=sqrt(Y/p)/(2*l) \n", + "print \"The frequency, n = %0.e vibrations/s \" %n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The frequency, n = 1e+04 vibrations/s \n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6, page 411" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Area of cross section\n", + "#given data :\n", + "n1BYn2=20 \n", + "T=20*9.8 # in N\n", + "Y=19.6*10**10 # in N/m**2\n", + "alfa=n1BYn2**2*T/Y \n", + "print \"Area of cross section, alfa = %0.e m^2 \" %alfa" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Area of cross section, alfa = 4e-07 m^2 \n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7, page 412" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Velocity and Young modulus\n", + "#given data :\n", + "n=2600 # in Hz\n", + "l=1 # in m\n", + "p=7.8*10**3 # kg/m**3\n", + "v=2*n*l \n", + "print \"The velocity, v = %0.f m/s \" % v\n", + "Y=v**2*p \n", + "print \"Youngs modulus, Y = %0.2e N/m^2 \" %Y" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The velocity, v = 5200 m/s \n", + "Youngs modulus, Y = 2.11e+11 N/m^2 \n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8, page 412" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Frequencies\n", + "#given data :\n", + "Y=7.1*10**10 # in N/m**2\n", + "p=2700 #in kg/m**3\n", + "l=1.5 # in m\n", + "r1=1 \n", + "r2=3 \n", + "r3=5 \n", + "n1=(r1/(4*l))*sqrt(Y/p) \n", + "n2=(r2/(4*l))*sqrt(Y/p) \n", + "n3=(r3/(4*l))*sqrt(Y/p) \n", + "print \"Frequency of first harmonic, n1 = %0.2f Hz \" %n1\n", + "print \"Frequency of second harmonic, n2 = %0.2f Hz \" %n2\n", + "print \"Frequency of third harmonic, n3 = %0.2f Hz \" %n3" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Frequency of first harmonic, n1 = 854.67 Hz \n", + "Frequency of second harmonic, n2 = 2564.00 Hz \n", + "Frequency of third harmonic, n3 = 4273.33 Hz \n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9, page 428" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi\n", + "# Frequency\n", + "#given data :\n", + "l=1.2 # in m\n", + "v=5150 # in m/s\n", + "d=0.006 # in m\n", + "k=d/sqrt(12) \n", + "v1=pi*v*k*3.011**2/(8*l**2) \n", + "print \"The frequency, v1 = %0.2f Hz \" %v1" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The frequency, v1 = 22.05 Hz \n" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10, page 429" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi\n", + "# Frequencies\n", + "#given data :\n", + "l=2 # in m\n", + "v=3560 # in m/s\n", + "r=0.004 # in m\n", + "k=r/2 \n", + "v1=pi*v*k*3.011**2/(8*l**2) \n", + "print \"The frequency, v1 = %0.2f Hz \" %v1\n", + "v2=pi*v*k*5**2/(8*l**2) \n", + "print \"The frequency of first overtone, v2 = %0.2f Hz\" %v2\n", + "v3=pi*v*k*7**2/(8*l**2) \n", + "print \"The frequency of second overtone, v3 = %0.2f Hz\" %v3" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The frequency, v1 = 6.34 Hz \n", + "The frequency of first overtone, v2 = 17.48 Hz\n", + "The frequency of second overtone, v3 = 34.25 Hz\n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11, page 429" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Frequency\n", + "#given data :\n", + "Y=7.1*10**10 # in N/m**2\n", + "p=2.7*10**3 # in kg/m**3\n", + "r=0.005 # in m\n", + "vu=sqrt(Y/p) \n", + "k=r/2 \n", + "v=vu/(2*pi*k) \n", + "print \"The frequency, v = %0.2e Hz \" %v" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The frequency, v = 3.26e+05 Hz \n" + ] + } + ], + "prompt_number": 20 + } + ], + "metadata": {} + } + ] +} diff --git a/Oscillations_and_Waves_by_S._Prakash/chapter11.ipynb b/Oscillations_and_Waves_by_S._Prakash/chapter11.ipynb new file mode 100755 index 00000000..f6794e5d --- /dev/null +++ b/Oscillations_and_Waves_by_S._Prakash/chapter11.ipynb @@ -0,0 +1,143 @@ +{ + "metadata": { + "name": "", + "signature": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 11, Lissajous' Figures " + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1, page 448" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Frequencies\n", + "#given data :\n", + "t=2.0 # in sec\n", + "n1=100.0 # in vibrations/sec\n", + "n2a=n1+(1/t) \n", + "n2b=n1-(1/t) \n", + "print \"Frequency, n2a = %0.2f \" %n2a\n", + "print \"frequency, n2b = %0.2f \"%n2b" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Frequency, n2a = 100.50 \n", + "frequency, n2b = 99.50 \n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2, page 448" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from __future__ import division\n", + "# Frequencies\n", + "#given data :\n", + "t1=15 # in sec\n", + "t2=10 # in sec\n", + "n2=400 # in vibrations/sec\n", + "n1a=n2+(1/t1) \n", + "n1b=n2-(1/t1) \n", + "print \"Frequency, n1a = %0.2f Hz \" %n1a\n", + "print \"Frequency, n1b = %0.2f Hz \" %n1b\n", + "n_1a=n2+(1/t2) \n", + "n_1b=n2-(1/t2) \n", + "print \"Frequency, n_1a = %0.2f Hz \" %n_1a\n", + "print \"Frequency, n_1b = %0.2f Hz \" %n_1b" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Frequency, n1a = 400.07 Hz \n", + "Frequency, n1b = 399.93 Hz \n", + "Frequency, n_1a = 400.10 Hz \n", + "Frequency, n_1b = 399.90 Hz \n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3, page 449" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Frequencies\n", + "#given data :\n", + "t1=15 # in sec\n", + "t2=10 # in sec\n", + "n2=256 # in vibrations/sec\n", + "n1a=(2*n2)+(1/t1) \n", + "n1b=(2*n2)-(1/t1) \n", + "print \"Frequency, n1a = %0.2f Hz \" %n1a\n", + "print \"Frequency, n1b = %0.2f Hz \" %n1b\n", + "n_1a=(2*n2)+(1/t2) \n", + "n_1b=(2*n2)-(1/t2) \n", + "print \"Frequency, n_1a = %0.2f Hz \" %n_1a\n", + "print \"Frequency, n_1b = %0.2f Hz \" %n_1b" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Frequency, n1a = 512.07 Hz \n", + "Frequency, n1b = 511.93 Hz \n", + "Frequency, n_1a = 512.10 Hz \n", + "Frequency, n_1b = 511.90 Hz \n" + ] + } + ], + "prompt_number": 7 + } + ], + "metadata": {} + } + ] +} diff --git a/Oscillations_and_Waves_by_S._Prakash/chapter12.ipynb b/Oscillations_and_Waves_by_S._Prakash/chapter12.ipynb new file mode 100755 index 00000000..ba23123e --- /dev/null +++ b/Oscillations_and_Waves_by_S._Prakash/chapter12.ipynb @@ -0,0 +1,524 @@ +{ + "metadata": { + "name": "", + "signature": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 12, Doppler's Effect" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1, page 457" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from __future__ import division\n", + "# Speed\n", + "#given data :\n", + "vl=166 #m/s\n", + "v=(2*vl) #m/s\n", + "print \"Speed = %0.f m/s \" %v" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Speed = 332 m/s \n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2, page 458" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# frequency\n", + "#given data :\n", + "f1=90 #vibrations/second\n", + "f2=(1+(1/10))*f1 #vibrations/s\n", + "print \"Frequency = %0.f vibrations/s \"%f2" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Frequency = 99 vibrations/s \n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3, page 458" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# frequency\n", + "#given data :\n", + "N=400 #hZ\n", + "V=340 #M/S\n", + "VS=60 #M/S\n", + "N2=((V/(V-VS))*N) #Hz\n", + "print \"Frequency when engine is approaching to the listner = %0.f Hz \" %round(N2)\n", + "N3=((V/(V+VS))*N) #Hz\n", + "print \"Frequency when engine is moving away from the listner = %0.f Hz \" %N3" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Frequency when engine is approaching to the listner = 486 Hz \n", + "Frequency when engine is moving away from the listner = 340 Hz \n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4, page 459" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#WAVELENGTH\n", + "x=1/5 #\n", + "h=60 #cm\n", + "h1=((1-x)*h) #cm\n", + "h2=((1+x)*h) #cm\n", + "print \"Wavelength of waves in north-direction = %0.f cm \" %h1\n", + "print \"Wavelength of waves in south-direction = %0.f cm\" %h2" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Wavelength of waves in north-direction = 48 cm \n", + "Wavelength of waves in south-direction = 72 cm\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5, page 460" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#frequency\n", + "v=340 #m/s\n", + "n=600 #Hz\n", + "vs=36 #km h**-1\n", + "vs1=vs*(1000/3600) #m/s\n", + "apf=((v)/(v-vs1))*n #Hz\n", + "vs2=54 #km h**-1\n", + "vs3=vs2*(1000/3600) #m/s\n", + "apf1=((v)/(v+vs3))*n #Hz\n", + "print \"Two apparent frequencies are\",round(apf,1),\"Hz and\",round(apf1,2),\"Hz.\"\n", + "df=apf-apf1 #Hz\n", + "print \"Difference in frequencies = %0.2f Hz\" %df\n", + "#second apparent frequency and difference is calculated wrong in the textbook" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Two apparent frequencies are 618.2 Hz and 574.65 Hz.\n", + "Difference in frequencies = 43.53 Hz\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6, page 460" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#frequency\n", + "v=330 #m/s\n", + "n=500 #Hz\n", + "vs=30 #km h**-1\n", + "vs1=vs*(1000/3600) #m/s\n", + "n3=((v+vs1)/(v-vs1))*n #Hz\n", + "print \"Frequency when cars are approaching = %0.f Hz \" %round(n3)\n", + "n1=((v-vs1)/(v+vs1))*n #Hz\n", + "print \"Frequency when cars have crossed = %0.f Hz\" %round(n1)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Frequency when cars are approaching = 526 Hz \n", + "Frequency when cars have crossed = 475 Hz\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7, page 461" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#frequency\n", + "v=330 #m/s\n", + "n=600 #Hz\n", + "vs=20 #m/s\n", + "apf=((v)/(v+vs))*n #Hz\n", + "print \"Frequency when source is moving away from the observer = %0.f Hz \" %round(apf)\n", + "apf1=((v)/(v-vs))*n #Hz\n", + "print \"Frequency when siren reaching at the cliff = %0.f Hz \" %round(apf1)\n", + "bf=apf1-apf #Hz\n", + "print \"Beat frequency = %0.f Hz \" %round(bf)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Frequency when source is moving away from the observer = 566 Hz \n", + "Frequency when siren reaching at the cliff = 639 Hz \n", + "Beat frequency = 73 Hz \n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8, page 461" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi\n", + "#frequency\n", + "r=3 #m\n", + "w=10 #s**-1\n", + "vs=r*w #m/s\n", + "A=6 #m\n", + "fd=5/pi #s**-1\n", + "vmax=A*2*pi*fd #m/s\n", + "v=330 #m/s\n", + "n=340 #Hz\n", + "nmax=((v+vmax)/(v-vs))*n #Hz\n", + "nmin=((v-vmax)/(v+vs))*n #Hz\n", + "print \"Maximum frequency = %0.f Hz \" %nmax\n", + "print \"Minimum frequency = %0.f Hz \" %nmin" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Maximum frequency = 442 Hz \n", + "Minimum frequency = 255 Hz \n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9, page 462" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#speed\n", + "n12=3 #\n", + "n=340 #Hz\n", + "v=340 #m/s\n", + "vs=((n12*v)/(2*n)) #m/s\n", + "print \"Speed = %0.2f m/s \" %vs" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Speed = 1.50 m/s \n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10, page 463" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt\n", + "#frequency\n", + "sa=1.5 #km\n", + "oa=1 #km\n", + "so=sqrt(oa**2+sa**2) #km\n", + "csd=sa/so #\n", + "v=0.33 #km/s\n", + "n=400 #Hz\n", + "vlov=120*(1000/3600) #m/s\n", + "vs1=(1/30)*csd #km/s\n", + "nd=((v)/(v-vs1))*n #vibrations/sec\n", + "print \"Apparent frequency = %0.f vibrations/second \" %round(nd)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Apparent frequency = 437 vibrations/second \n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11, page 464" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#frequency\n", + "v=1200 #km/h\n", + "w=40 #km/h\n", + "vs=40 #km/h\n", + "n=580 #Hz\n", + "nd=((v+vs)/((v+vs)-vs))*n #Hz\n", + "print \"Frequency of the whistle as heared by an observer on the hill = %0.2f Hz \" %nd\n", + "x=29/30 #km\n", + "print \"Distance = %0.2f m \" %(x*1000)\n", + "ndd=((v-w)+vs)/((v-w))*nd #Hz\n", + "print \"Frequency heared by driver = %0.2f Hz \" %ndd\n", + "#distance is calculated wrong in the textbook" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Frequency of the whistle as heared by an observer on the hill = 599.33 Hz \n", + "Distance = 966.67 m \n", + "Frequency heared by driver = 620.00 Hz \n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12, page 469" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#doppler shift and velocity\n", + "h1=6010 #\u00c5\n", + "h2=6000 #\u00c5\n", + "ds=h1-h2 #\u00c5\n", + "print \"Doppler shift = %0.f \u00c5 \" %ds\n", + "c=3*10**8 #m/s\n", + "v=((ds/h2)*c) #m/s\n", + "print \"Speed = %0.e m/s \" %v" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Doppler shift = 10 \u00c5 \n", + "Speed = 5e+05 m/s \n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13, page 469" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#doppler shift and velocity\n", + "h1=3737 #\u00c5\n", + "h2=3700 #\u00c5\n", + "ds=h1-h2 #\u00c5\n", + "print \"Doppler shift = %0.f \u00c5 \" %ds\n", + "c=3*10**8 #m/s\n", + "v=((ds/h2)*c) #m/s\n", + "print \"Speed = %0.e m/s \" %v\n", + "#speed is calculated wrong in the textbook" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Doppler shift = 37 \u00c5 \n", + "Speed = 3e+06 m/s \n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14, page 469" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#speed\n", + "dv=10**3 #Hz\n", + "v=5*10**9 #Hz\n", + "c=3*10**8 #m/s\n", + "v=((dv)/(2*v))*c #m/s\n", + "print \"Velocity = %0.f m/s \" %v" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Velocity = 30 m/s \n" + ] + } + ], + "prompt_number": 19 + } + ], + "metadata": {} + } + ] +} diff --git a/Oscillations_and_Waves_by_S._Prakash/chapter13.ipynb b/Oscillations_and_Waves_by_S._Prakash/chapter13.ipynb new file mode 100755 index 00000000..6c8b227d --- /dev/null +++ b/Oscillations_and_Waves_by_S._Prakash/chapter13.ipynb @@ -0,0 +1,104 @@ +{ + "metadata": { + "name": "", + "signature": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 13, Elementary theory of filters" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1, page 491" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from __future__ import division\n", + "from math import pi\n", + "# design loss pass constant K-filter\n", + "k=600 #ohms\n", + "fc=2500 #Hz\n", + "l=(k/(pi*fc)) #H\n", + "c=((1/(pi*fc*k))) #farad\n", + "print \"Inductance = %0.1f mH\" %(l*10**3)\n", + "print \"Capacitance = %0.3f micro-F \" %(c*10**6)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Inductance = 76.4 mH\n", + "Capacitance = 0.212 micro-F \n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2, page 492" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi\n", + "#T-type band pass filter\n", + "#given data :\n", + "K=500 # in ohm\n", + "f1=4 # in kHz\n", + "f2=1 # in kHz\n", + "L1=K/(pi*(f1-f2)) \n", + "Ls=L1/2 \n", + "print \"Inductance in each series arm, Ls = %0.2f mH \" %Ls\n", + "C1=(f1-f2)*10**3/(4*pi*K*f1*f2) \n", + "Cs=2*C1 \n", + "print \"Capacity in each series arm, Cs = %0.2f micro-F\" %Cs\n", + "L2=((f1-f2)*K*1e3)/(4*pi*f1*f2*1e6)*1e3 # mH\n", + "print \"Shunt arm inductance, L2 = %0.1f mH\" %L2\n", + "Csh=1*10**6/(pi*(f1-f2)*10**3*K) \n", + "print \"Capacity in shunt arm, Csh = %0.2f micro-F\" % Csh" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Inductance in each series arm, Ls = 26.53 mH \n", + "Capacity in each series arm, Cs = 0.24 micro-F\n", + "Shunt arm inductance, L2 = 29.8 mH\n", + "Capacity in shunt arm, Csh = 0.21 micro-F\n" + ] + } + ], + "prompt_number": 13 + } + ], + "metadata": {} + } + ] +} diff --git a/Oscillations_and_Waves_by_S._Prakash/chapter14.ipynb b/Oscillations_and_Waves_by_S._Prakash/chapter14.ipynb new file mode 100755 index 00000000..fe26f3cb --- /dev/null +++ b/Oscillations_and_Waves_by_S._Prakash/chapter14.ipynb @@ -0,0 +1,155 @@ +{ + "metadata": { + "name": "", + "signature": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 14, Ultrasonics" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1, page 510" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from __future__ import division\n", + "# Fundamental frequency\n", + "#given data :\n", + "t=1.6*10**-3 # in m\n", + "lamda=2*t # in m\n", + "v=5760 # in m/s\n", + "n1=v*10**-6/lamda \n", + "print \"Fundamental frequency, n1 = %0.2f MHz \" %n1" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Fundamental frequency, n1 = 1.80 MHz \n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2, page 510" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# distance\n", + "#given data :\n", + "th=40 #cm\n", + "t1=30 #micro-seconds\n", + "t2=80 #micro seconds\n", + "x=((2*th*10**-2*t1*10**-6)/(2*t2*10**-6))*100 #cm\n", + "print \"Distance %0.2f cm \" %x" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Distance 15.00 cm \n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3, page 510" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Thickness\n", + "#given data :\n", + "v=5000 # in m/s\n", + "N=50000 # in Hz\n", + "t=v/(2*N) \n", + "print \"Thickness of steel plate, t = %0.2f m \" %t" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Thickness of steel plate, t = 0.05 m \n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4, page " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi\n", + "# Capacitance\n", + "#given data :\n", + "L=1 # in H\n", + "n=10**6 # in Hz\n", + "C=1*10**12/(4*pi**2*n**2*L) \n", + "print \"The capacitance, C = %0.3f micro-F \" %C" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The capacitance, C = 0.025 micro-F \n" + ] + } + ], + "prompt_number": 6 + } + ], + "metadata": {} + } + ] +} diff --git a/Oscillations_and_Waves_by_S._Prakash/chapter15.ipynb b/Oscillations_and_Waves_by_S._Prakash/chapter15.ipynb new file mode 100755 index 00000000..da8ea509 --- /dev/null +++ b/Oscillations_and_Waves_by_S._Prakash/chapter15.ipynb @@ -0,0 +1,126 @@ +{ + "metadata": { + "name": "", + "signature": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 15, Musical sound & acoustic of buildings" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1, page 518" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from __future__ import division\n", + "from math import log10\n", + "# decibles\n", + "#given data :\n", + "i1=4 #assume\n", + "i2=4*i1 #\n", + "dl=10*log10(i2/i1) #db\n", + "print \"Decibles by which intensity level will decrease = %0.2f db \" %dl" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Decibles by which intensity level will decrease = 6.02 db \n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2, page 519" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import sympy\n", + "# ratio of amlitudes\n", + "#given data :\n", + "l1=10 #db\n", + "l2=40 #db\n", + "dl=l2-l1 #db\n", + "x=(10**(dl/10)) #\n", + "x1=sympy.sqrt(x) #\n", + "print \"Ratio of amplitudes =\", x1" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Ratio of amplitudes = 10*sqrt(10)\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3, page 521" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# frequency\n", + "#given data :\n", + "x=264 #key note\n", + "g=x*(3.0/2) #\n", + "print \"Frequency of note G = %0.f \" %g\n", + "cd1=x*2 #\n", + "print \"Frequency of note C = %0.f \"%cd1" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Frequency of note G = 396 \n", + "Frequency of note C = 528 \n" + ] + } + ], + "prompt_number": 3 + } + ], + "metadata": {} + } + ] +} diff --git a/Oscillations_and_Waves_by_S._Prakash/chapter17.ipynb b/Oscillations_and_Waves_by_S._Prakash/chapter17.ipynb new file mode 100755 index 00000000..d7df3137 --- /dev/null +++ b/Oscillations_and_Waves_by_S._Prakash/chapter17.ipynb @@ -0,0 +1,246 @@ +{ + "metadata": { + "name": "", + "signature": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 17, Electromagnetic waves" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1, page 550" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from __future__ import division\n", + "from numpy import pi\n", + "# magnitude\n", + "#given data :\n", + "R=7*10**8 # in m\n", + "P=3.8*10**26 # in Watt\n", + "S=P/(4*pi*R**2) \n", + "print \"Magnitude of poynting vector, S = %0.3e W/m^2 \" %S" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Magnitude of poynting vector, S = 6.171e+07 W/m^2 \n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2, page 551" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from numpy import pi\n", + "# Poynting vector\n", + "#given data :\n", + "R=1.5*10**11 # in m\n", + "P=3.8*10**26 # in Watt\n", + "S=P/(4*pi*R**2) # in W/m**2\n", + "Se=round(S*60/(4.2*10**4)) \n", + "print \"Poynting vector, Se = %0.2f cal/cm^2-m \" %Se" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Poynting vector, Se = 2.00 cal/cm^2-m \n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3, page 560" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from numpy import sqrt\n", + "# Amplitude and magnetic field\n", + "#given data :\n", + "S=2 # in cal/cm**2- min\n", + "EH=S*4.2*10**4/60 # joule/m**2 sec\n", + "mu0=4*pi*10**-7 \n", + "epsilon0=8.85*10**-12 \n", + "EbyH=sqrt(mu0/epsilon0) \n", + "E=sqrt(EH*EbyH) \n", + "H=EH/E \n", + "E0=E*sqrt(2) \n", + "H0=H*sqrt(2) \n", + "print \"E = %0.2f V/m \"%E\n", + "print \"H = %0.3f Amp-turn/m \"%H\n", + "print \"Amplitude of electric fields of radiation, E0 = %0.f V/m \" %E0\n", + "print \"Magnetice field of radition, H0 = %0.2f Amp-turn/m \" %H0" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "E = 726.32 V/m \n", + "H = 1.928 Amp-turn/m \n", + "Amplitude of electric fields of radiation, E0 = 1027 V/m \n", + "Magnetice field of radition, H0 = 2.73 Amp-turn/m \n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4, page 560" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from numpy import pi\n", + "# electric and magnetic field\n", + "#given data :\n", + "r=2 # in m\n", + "mu0=4*pi*10**-7 \n", + "epsilon0=8.85*10**-12 \n", + "EbyH=sqrt(mu0/epsilon0) \n", + "EH=1000/(4*r**2*pi**2) # in W/m**2\n", + "E=sqrt(EH*EbyH) \n", + "H=(EH/E) \n", + "print \"Intensities of electric, E = %0.2f V/m\" %E\n", + "print \"Magnetic field of radiation, H = %0.4f Amp-turn/m \" %H" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Intensities of electric, E = 48.85 V/m\n", + "Magnetic field of radiation, H = 0.1296 Amp-turn/m \n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5, page 593" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import degrees, pi, asin, sin, tan\n", + "# Degree of polarization\n", + "#given data :\n", + "thetai=45 # in degree\n", + "n=1.5 #/ index\n", + "thetar=asin(sin(thetai*pi/180)/n) # radian\n", + "thetar= degrees(thetar)\n", + "Rl=sin((thetai-thetar)*pi/180)**2/sin((thetai+thetar)*pi/180)**2 \n", + "Rp=tan(thetai-thetar*pi/180)**2/tan((thetai+thetar)*pi/180)**2 \n", + "D=((Rl-Rp)/(Rl+Rp))*100 \n", + "print \"Degree of polarization, D = %0.2f %%\" %D\n", + "# answer is wrong in the textbook" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Degree of polarization, D = 49.44 %\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6, page 594" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Frequency\n", + "#given data :\n", + "Del=1 # in m\n", + "mu=4*pi*10**-7 # in H/m\n", + "sigma=4 # in siemen/m\n", + "v=1*10**-3/(pi*Del**2*mu*sigma) \n", + "print \"Frequency, v = %0.1f kHz \" %v" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Frequency, v = 63.3 kHz \n" + ] + } + ], + "prompt_number": 16 + } + ], + "metadata": {} + } + ] +} diff --git a/Oscillations_and_Waves_by_S._Prakash/chapter2.ipynb b/Oscillations_and_Waves_by_S._Prakash/chapter2.ipynb new file mode 100755 index 00000000..b64a947b --- /dev/null +++ b/Oscillations_and_Waves_by_S._Prakash/chapter2.ipynb @@ -0,0 +1,450 @@ +{ + "metadata": { + "name": "", + "signature": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 2, Damped harmonic oscillator" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3, page 102" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from __future__ import division\n", + "from math import log\n", + "# relaxation time ,damping force ,time and total distance\n", + "v=10 #cm/s\n", + "vo=100 #cm/s\n", + "t=23 #sec\n", + "x=-(log(v/vo))/t #\n", + "t=(1/x)*1 #seconds\n", + "print \"Relaxation time = %0.f seconds \" %t\n", + "m=40 #gm\n", + "vx=50 #cm/sec\n", + "fd=((-x*m*10**-3*vx*10**-2)) #newton\n", + "print \"Damping force = %0.e N\" %fd\n", + "tx=5*(log(10)) #\n", + "print \"Time in which kinetic energy will reduce to 1/10th of its value = %0.1f seconds \" %tx\n", + "xx=v*1 #\n", + "print \"Distance travelled = %0.f m \" %xx" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Relaxation time = 10 seconds \n", + "Damping force = -2e-03 N\n", + "Time in which kinetic energy will reduce to 1/10th of its value = 11.5 seconds \n", + "Distance travelled = 10 m \n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4, page 104" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt, pi\n", + "# period\n", + "#given data :\n", + "m=2 # in g\n", + "k=30 # in dynes/cm\n", + "b=5 # in dynes/cm-sec**-1\n", + "r=b/(2*m) \n", + "w0=sqrt(k/m) \n", + "T=2*pi/sqrt(w0**2-r**2) \n", + "print \"The time period, T = %0.2f s \" %T" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The time period, T = 1.71 s \n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5, page 105" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# time\n", + "tr=50 #seconds\n", + "r=(1/(2*tr)) #s**-1\n", + "t=1/r #seconds\n", + "print \"Time in which amplitude falls to 1/e times the initial value = %0.f seconds \" %t\n", + "t2=tr #\n", + "print \"Time in which system falls to 1/e times the initial value = %0.f seconds\" %t2\n", + "t3=2*(1/r) #f \n", + "print \"Time in which energy falls to 1/e^4 of the initial value = %0.f seconds \" %t3" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Time in which amplitude falls to 1/e times the initial value = 100 seconds \n", + "Time in which system falls to 1/e times the initial value = 50 seconds\n", + "Time in which energy falls to 1/e^4 of the initial value = 200 seconds \n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6, page 106" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt, pi\n", + "import sympy\n", + "# relaxation time ,frequency ,energy ,time ,rate and number of vibrations\n", + "k=20 #N/m\n", + "m=5#N-s/m\n", + "wo=sqrt(k/m) #\n", + "v1=2 #m/s\n", + "to=m/v1 #seconds\n", + "print \"(a) Relaxation time = %0.1f seconds \" %to\n", + "w=wo*(1-(1/(2*wo*to))**2) #\n", + "lf=w/(2*pi) #vibration/s\n", + "print \"(b) Linear frequency = %0.3f vibration/s \" %lf\n", + "a=1 #\n", + "e=((1/2)*m*a**2*wo**2) #joule\n", + "print \"(c) Energy = %0.f J \"%e\n", + "tm=v1*to #seconds\n", + "print \"(d) Time taken in fall of amlitude to 1/e value = %0.f seconds \" %tm\n", + "print \"(e) Time taken in fall of velocity amplitude to 1/2 value = %0.f seconds \" %tm\n", + "tr=to #\n", + "print \"(f) Time taken in fall of energy to 1/e value = %0.2f seconds\" %tr\n", + "eng=(1/2)*m*a*v1**2*(2/tm) #\n", + "print \"(g) Rate of loss of energy at t=0 seconds is\",eng,\"J/s and at any time is\",eng,\"e^-2*t/\",tm,\"J/s\"\n", + "rel=((eng*2*pi)/wo) #J/s\n", + "print \"(h) Rate of loss of energy per cycle at t=0 seconds is\",rel,\"J/s and at any time is\",round(rel,2),\"e^-2*t/\",tm,\"J/s\"\n", + "nv=tm/((2*sympy.pi)/wo) #\n", + "print \"(i) Number of vibratios made are =\",nv" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(a) Relaxation time = 2.5 seconds \n", + "(b) Linear frequency = 0.315 vibration/s \n", + "(c) Energy = 10 J \n", + "(d) Time taken in fall of amlitude to 1/e value = 5 seconds \n", + "(e) Time taken in fall of velocity amplitude to 1/2 value = 5 seconds \n", + "(f) Time taken in fall of energy to 1/e value = 2.50 seconds\n", + "(g) Rate of loss of energy at t=0 seconds is 4.0 J/s and at any time is 4.0 e^-2*t/ 5.0 J/s\n", + "(h) Rate of loss of energy per cycle at t=0 seconds is 12.5663706144 J/s and at any time is 12.57 e^-2*t/ 5.0 J/s\n", + "(i) Number of vibratios made are = 5.0/pi\n" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7, page 109" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# time and distance\n", + "b=5 #N-s/m\n", + "v=10 #m/s\n", + "to=b/v #second\n", + "print \"(a) Time in which velocity falls to 1/e times the initial value = %0.2f second \" %to\n", + "t2=b*to #\n", + "print \"(b) Time in which velocity falls to half the initial value = %0.2f second \" %t2\n", + "print \"(c) Distance traversed by the particle before the velocity falls to half the initial value is\",b,\"*(1-exp(log)\",(2*to)/to\n", + "x=b #m\n", + "print \"(d) Distance traversed by the particle it comes to rest = %0.2f m \" %x" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(a) Time in which velocity falls to 1/e times the initial value = 0.50 second \n", + "(b) Time in which velocity falls to half the initial value = 2.50 second \n", + "(c) Distance traversed by the particle before the velocity falls to half the initial value is 5 *(1-exp(log) 2.0\n", + "(d) Distance traversed by the particle it comes to rest = 5.00 m \n" + ] + } + ], + "prompt_number": 25 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8, page 111" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import log, pi\n", + "# time interval\n", + "q=5*10**4 #quality factor\n", + "x=1/10 #\n", + "fr=300 #second**-1\n", + "to=q/(2*pi*fr) #second\n", + "xm=((to*log(10))) #seconds\n", + "print \"Time interval = %0.f seconds \" %xm" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Time interval = 61 seconds \n" + ] + } + ], + "prompt_number": 27 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9, page 111" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Time\n", + "#given data :\n", + "n=240 # in sec**-1\n", + "w=2*pi*n \n", + "Q=2*10**3 \n", + "tau=Q/w \n", + "t=4*tau \n", + "print \"Time, t = %0.1f s \" %t" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Time, t = 5.3 s \n" + ] + } + ], + "prompt_number": 29 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10, page 112" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import log\n", + "# Logarithmic decrement\n", + "#given data :\n", + "a=100 \n", + "l1=20 # in cm\n", + "l2=2 # in cm\n", + "l=l1/l2 \n", + "lamda=(1/100)*log(l) \n", + "print \" Logarithmic decrement = %0.3f \" %lamda" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " Logarithmic decrement = 0.023 \n" + ] + } + ], + "prompt_number": 31 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12, page 116" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt, pi\n", + "# Frequency\n", + "#given data :\n", + "C=10**-6 # in F\n", + "L=0.2 # in H\n", + "R=800 # in ohm\n", + "Rm=2*sqrt(L/C) \n", + "n=sqrt((1/(L*C))-(R**2/(4*L**2)))/(2*pi) \n", + "print \"The frequency, n = %0.1f cycles/s \" %n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The frequency, n = 159.2 cycles/s \n" + ] + } + ], + "prompt_number": 33 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13, page 116" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt\n", + "# Resistance\n", + "#given data :\n", + "C=0.0012*10**-6 # in F\n", + "L=0.2 # in H\n", + "Rm=2*sqrt(L/C) \n", + "print \"The maximum value of resistance, Rm = %0.2e ohms \" %Rm" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The maximum value of resistance, Rm = 2.58e+04 ohms \n" + ] + } + ], + "prompt_number": 35 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 14, page 117" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt, pi\n", + "# Q factor\n", + "#given data :\n", + "C=5*10**-6 # in F\n", + "L=2*10**-3 # in H\n", + "R=0.2 # in ohm\n", + "w=round(sqrt((1/(L*C))-(R**2/(4*L**2)))) \n", + "f=w/(2*pi) \n", + "Q=w*L/R \n", + "print \"Frequency = %0.2e Hz \" %f\n", + "print \"Quality factor, Q = %0.f \" %Q" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Frequency = 1.59e+03 Hz \n", + "Quality factor, Q = 100 \n" + ] + } + ], + "prompt_number": 38 + } + ], + "metadata": {} + } + ] +} diff --git a/Oscillations_and_Waves_by_S._Prakash/chapter3.ipynb b/Oscillations_and_Waves_by_S._Prakash/chapter3.ipynb new file mode 100755 index 00000000..2411d4be --- /dev/null +++ b/Oscillations_and_Waves_by_S._Prakash/chapter3.ipynb @@ -0,0 +1,226 @@ +{ + "metadata": { + "name": "", + "signature": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 3, Forced harmonic oscillator & resonance" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1, page 135" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from __future__ import division\n", + "from math import sqrt, degrees, atan, pi\n", + "# Phase shift\n", + "#given data :\n", + "F0=25 # in N\n", + "m=1 \n", + "f0=F0/m \n", + "K=1*10**3 # in N/m\n", + "w0=sqrt(K/m) \n", + "b=0.05 # in N-s/m\n", + "r=b/(2*m) # in s**-1\n", + "A=f0*10**3/sqrt(9*w0**4+(16*r**2*(w0)**2)) \n", + "print \"The amplitude, A = %0.2f mm \" %A\n", + "p=2*w0 \n", + "fi=atan(2*r*p/(w0**2-p**2)) # radian \n", + "fi = degrees(fi) # degree\n", + "print \"Phase shift is\",round(fi,2),\"degree or\",round(fi*(pi/180),3),\"radian.\"\n", + "#phase shift is converted wrong into radians" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The amplitude, A = 8.33 mm \n", + "Phase shift is -0.06 degree or -0.001 radian.\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2, page 136" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from numpy import array\n", + "# A/Amax\n", + "x1=array([0.99,0.98,0.97]) #\n", + "wt=50 #\n", + "wo=1 #assume\n", + "fo=1 #assume\n", + "for x in x1:\n", + " a=((fo/((wo**2)*((1-x**2)**2+((1/wt**2)*x**2))**(1/2)))) #\n", + " am=fo/((wo**2)*(1/wt**2)**(1/2)) #\n", + " z=a/am #\n", + " print \"For p/wo\",x,\", value of A/Amax is\",round(z,2)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "For p/wo 0.99 , value of A/Amax is 0.71\n", + "For p/wo 0.98 , value of A/Amax is 0.45\n", + "For p/wo 0.97 , value of A/Amax is 0.32\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3, page 154" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi, sqrt\n", + "# Reactance and impedence\n", + "#given data :\n", + "n=50 # in cycles\n", + "w=2*pi*n # in rad/sec\n", + "L=1/pi # in H\n", + "XL=w*L \n", + "print \"The reactance, XL = %0.0f ohm \" %XL\n", + "R=100 # in ohm\n", + "Z=sqrt(R**2+XL**2) \n", + "print \"The impedence, Z = %0.1f ohm \" %Z" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The reactance, XL = 100 ohm \n", + "The impedence, Z = 141.4 ohm \n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4, page 155" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt, pi\n", + "# Current and Capacity\n", + "#given data :\n", + "E=110 # in V\n", + "R=10 # in ohm\n", + "L=1*10**-3 # in H\n", + "C=1*10**-6 # in F\n", + "n=10000 # in Hz\n", + "w=2*pi*n \n", + "I=E/sqrt(R**2+((w*L)-(1/(w*C)))**2) \n", + "print \"The current, I = %0.2f A \" %I\n", + "L1=1/(w**2*C) \n", + "print \"The value of capacity, L1 = %0.2e F \" %L1\n", + "#Capacitance is calculated wrong in the textbook" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The current, I = 2.29 A \n", + "The value of capacity, L1 = 2.53e-04 F \n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5, page 155" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt\n", + "# Resonent frequency and Separation\n", + "#given data :\n", + "L=1*10**-3 # in H\n", + "C=0.1*10**-6 # in F\n", + "w0=1/sqrt(L*C) \n", + "print \"Resonant frequency, w0 = %0.e rad/s \" %w0\n", + "R=10 # in ohm\n", + "w2_w1=R/L \n", + "print \"The separation = %0.e rad/s \" %w2_w1\n", + "S=w0/w2_w1 \n", + "print \"The sharpness = %0.f \" %S" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Resonant frequency, w0 = 1e+05 rad/s \n", + "The separation = 1e+04 rad/s \n", + "The sharpness = 10 \n" + ] + } + ], + "prompt_number": 16 + } + ], + "metadata": {} + } + ] +} diff --git a/Oscillations_and_Waves_by_S._Prakash/chapter4.ipynb b/Oscillations_and_Waves_by_S._Prakash/chapter4.ipynb new file mode 100755 index 00000000..062db23c --- /dev/null +++ b/Oscillations_and_Waves_by_S._Prakash/chapter4.ipynb @@ -0,0 +1,57 @@ +{ + "metadata": { + "name": "", + "signature": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 4, Coupled oscillators" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2, page 195" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from __future__ import division\n", + "# ratio of Frequency\n", + "k=1 #assume\n", + "m1=16 #a.m.u\n", + "m2=12 #a.m.u\n", + "m3=m1 #\n", + "rt=((m2+2*m1)/m2)**(1/2) #\n", + "print \"Ratio of frequency = %0.2f \" %rt" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Ratio of frequency = 1.91 \n" + ] + } + ], + "prompt_number": 1 + } + ], + "metadata": {} + } + ] +} diff --git a/Oscillations_and_Waves_by_S._Prakash/chapter5.ipynb b/Oscillations_and_Waves_by_S._Prakash/chapter5.ipynb new file mode 100755 index 00000000..103201f7 --- /dev/null +++ b/Oscillations_and_Waves_by_S._Prakash/chapter5.ipynb @@ -0,0 +1,661 @@ +{ + "metadata": { + "name": "", + "signature": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "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": {} + } + ] +} diff --git a/Oscillations_and_Waves_by_S._Prakash/chapter7.ipynb b/Oscillations_and_Waves_by_S._Prakash/chapter7.ipynb new file mode 100755 index 00000000..c30a0e68 --- /dev/null +++ b/Oscillations_and_Waves_by_S._Prakash/chapter7.ipynb @@ -0,0 +1,579 @@ +{ + "metadata": { + "name": "", + "signature": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 7, Superposition of harmonic waves : Interference, Beats, Stationary waves, Phase and group velocities " + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1, page 272" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from __future__ import division\n", + "from numpy import sqrt\n", + "# ratio\n", + "ri=9/16 #ratio of intensities\n", + "ra=sqrt(ri) #ratio of amplitude\n", + "a1=1 #assume\n", + "a2=ra*a1 #\n", + "rim=(a1+a2)**2/(a1-a2)**2 #\n", + "print \"Ratio of maximum intensity and minimum intensity in fringe system is %d\"%rim,\":\",a1" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Ratio of maximum intensity and minimum intensity in fringe system is 49 : 1\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2, page 272" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import cos, pi\n", + "# intensity\n", + "I=1 #assume\n", + "a1=1*I #\n", + "a2=4*I #\n", + "ph1=0 #degree\n", + "i1=(a1+a2)+a2*cos(ph1*pi/180) #\n", + "print \"Intensity where phase difference is zero =\",i1,\"*I\"\n", + "ph2=90 #degree\n", + "i2=(a1+a2)+a2*cos(ph2*pi/180) #\n", + "print \"Intensity where phase difference is pi/2 =\",i2,\"*I\"\n", + "ph3=180 #degree\n", + "i3=(a1+a2)+a2*cos(ph3*pi/180) #\n", + "print \"Intensity where phase difference is pi is =\",i3,\"*I\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Intensity where phase difference is zero = 9.0 *I\n", + "Intensity where phase difference is pi/2 = 5.0 *I\n", + "Intensity where phase difference is pi is = 1.0 *I\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3, page 273" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Wavelength and frequency\n", + "#given data :\n", + "d=30 # in cm\n", + "lamda=2*d*10**-2 \n", + "v=330 # in m/s\n", + "print \"The wavelength = %0.2f m \" %lamda\n", + "n=v/lamda \n", + "print \"The frequency, n = %0.2f vibrations/s \" %n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The wavelength = 0.60 m \n", + "The frequency, n = 550.00 vibrations/s \n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4, page 281" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# number of beats and time interval\n", + "from fractions import Fraction\n", + "n1=300 #Hz\n", + "n2=303 #Hz\n", + "bfs=n2-n1 #\n", + "print \"Beat frequency = %0.2f per second \" %bfs\n", + "ti=Fraction(1/bfs).limit_denominator(3) #second\n", + "print \"Time interval =\",ti,\"second \"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " Beat frequency = 3.00 per second \n", + "Time interval = 1/3 second \n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5, page 281" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Frequency\n", + "#given data :\n", + "n1=256 # in Hz\n", + "x=4 # in beats per sec\n", + "n2a=n1+x \n", + "n2b=n1-x \n", + "print \"The frequency, n2a = %0.2f Hz \" %n2a\n", + "print \"The frequency, n2b = %0.2f Hz \"% n2b " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The frequency, n2a = 260.00 Hz \n", + "The frequency, n2b = 252.00 Hz \n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6, page 282" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Frequency\n", + "#given data :\n", + "nA=256 # in Hz\n", + "x=5 # in beats per sec\n", + "nB1=nA+x \n", + "nB2=nA-x \n", + "print \"The frequency, nB = %0.f Hz or %0.f Hz\" %(nB1, nB2)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The frequency, nB = 261 Hz or 251 Hz\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7, page 283" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Frequency\n", + "#given data :\n", + "nB=512 # in Hz\n", + "x=5 # in beats per sec\n", + "nA1=nB+x \n", + "nA2=nB-x \n", + "print \"The frequency of A, nA = %0.f Hz or %0.f Hz\" %(nA1, nA2)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The frequency of A, nA = 517 Hz or 507 Hz\n" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8, page 283" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Velocity of sound\n", + "#given data :\n", + "lamda1=1 # in m\n", + "lamda2=1.01 # in m\n", + "a=10/3 # in beats/sec\n", + "v=a/((lamda2-lamda1)/(lamda1*lamda2)) \n", + "print \"The velocity of sound, v = %0.1f m/s \" %v" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The velocity of sound, v = 336.7 m/s \n" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9, page 284" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Frequency\n", + "n=273 #\n", + "b1=4 #beats per second\n", + "b2=b1-1 #\n", + "t1=15 #degree celsius\n", + "t2=10 #degree celsius\n", + "v1510=sqrt((n+t1)/(n+t2)) #\n", + "n=((b2*v1510-b1)/(1-v1510)) #\n", + "print \"Frequency = %0.2f Hz \" %n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Frequency = 110.70 Hz \n" + ] + } + ], + "prompt_number": 20 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10, page 284" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Frequency\n", + "b1=10 #beats per second\n", + "f1=300 #Hz\n", + "b2=15 #beats per second\n", + "f2=325 #Hz\n", + "n1=f1-b1 #Hz\n", + "n2=f1+b1 #Hz\n", + "n3=f2-b2 #Hz\n", + "n4=f2+b2 #Hz\n", + "print \"Frequency = %0.2f Hz \" %n2" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Frequency = 310.00 Hz \n" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11, page 285" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Velocity of sound\n", + "#given data :\n", + "lamda1=5 # in m\n", + "lamda2=5.5 # in m\n", + "a=6 # beats/sec\n", + "v=a/((lamda2-lamda1)/(lamda1*lamda2)) \n", + "print \"The velocity of sound, v = %0.2f m/s \" %v" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The velocity of sound, v = 330.00 m/s \n" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12, page 285" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Frequency\n", + "b1=5 #beats per second\n", + "fr=384 #Hz\n", + "fo=fr-b1 #Hz\n", + "print \"Frequency = %0.2f Hz \" %fo" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Frequency = 379.00 Hz \n" + ] + } + ], + "prompt_number": 23 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13, page 285" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Frequency\n", + "b1=4 #beats per second\n", + "fr=256 #Hz\n", + "fo1=fr+b1 #Hz\n", + "fo2=fr-b1 #Hz\n", + "print \"Frequency = %0.f Hz or %0.f Hz\" %(fo1,fo2)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Frequency = 260 Hz or 252 Hz\n" + ] + } + ], + "prompt_number": 25 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 18, page 297" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Frequency,wavelength, velocity and amplitude\n", + "#given data :\n", + "a=6 # in cm\n", + "lamda=10 # in cm\n", + "T=1/10 # in sec\n", + "print \"Wavelength of progressive wave = %0.2f cm \" %lamda\n", + "n=1/T \n", + "print \"Frequency of progressive wave, n = %0.2f per sec \" %n\n", + "v=n*lamda \n", + "print \"The velocity, v = %0.2f cm/s \" %v\n", + "print \"The amplitude, a = %0.2f cm \" %a" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Wavelength of progressive wave = 10.00 cm \n", + "Frequency of progressive wave, n = 10.00 per sec \n", + "The velocity, v = 100.00 cm/s \n", + "The amplitude, a = 6.00 cm \n" + ] + } + ], + "prompt_number": 26 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 24, page 309" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Velocity\n", + "#given data :\n", + "c=3*10**8 # in m/s\n", + "lamda1=4000 # in Angustrom\n", + "lamda2=5000 # in Aungustrom\n", + "mu1=1.540 \n", + "mu2=1.530 \n", + "vg=c*((mu1*lamda1)-(mu2*lamda2))/(mu1*mu2*(lamda1-lamda2)) \n", + "print \"The velocity, vg = %0.3e m/s \" %vg" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The velocity, vg = 1.897e+08 m/s \n" + ] + } + ], + "prompt_number": 28 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 25, page 310" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Velocity\n", + "#given data :\n", + "v=1.8*10**8 # in m/s\n", + "lamda=3.6*10**-7 # in m\n", + "dv_dlamda=3.8*10**13 # in per sec\n", + "vg=v-(lamda*dv_dlamda) \n", + "print \"The group velocity, vg = %0.2e m/s \" %vg" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The group velocity, vg = 1.66e+08 m/s \n" + ] + } + ], + "prompt_number": 29 + } + ], + "metadata": {} + } + ] +} 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": {} + } + ] +} diff --git a/Oscillations_and_Waves_by_S._Prakash/chapter9.ipynb b/Oscillations_and_Waves_by_S._Prakash/chapter9.ipynb new file mode 100755 index 00000000..7e5e33c8 --- /dev/null +++ b/Oscillations_and_Waves_by_S._Prakash/chapter9.ipynb @@ -0,0 +1,493 @@ +{ + "metadata": { + "name": "", + "signature": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 9, Longitudinal acoustic waves in air" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1, page 380" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from __future__ import division\n", + "from math import pi\n", + "# Pressure amplitude, Energy density and Energy flux\n", + "#given data :\n", + "A=1*10**-5 # in m\n", + "n=500 # in per sec\n", + "v=340 # in m/s\n", + "p=1.29 # in kg/m**3\n", + "Pa=2*pi*n*v*p*A \n", + "print \"Pressure amplitude, Pa = %0.1f N/m^2 \"%Pa\n", + "Ed=2*pi**2*n**2*p*A**2 \n", + "print \"Energy density, Ed = %0.1e J/m^3 \" %Ed\n", + "Ev=Ed*v \n", + "print \"Energy flux, Ev = %0.2f J/m^2-s \" %Ev" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Pressure amplitude, Pa = 13.8 N/m^2 \n", + "Energy density, Ed = 6.4e-04 J/m^3 \n", + "Energy flux, Ev = 0.22 J/m^2-s \n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2, page 381" + ] + }, + { + "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": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3, page 381" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt\n", + "# The amplitude \n", + "#given data :\n", + "n=350 # in Hz\n", + "v=330 # in m/s\n", + "p=1.293 # in kg/m**3\n", + "I=1*10**-6 # in W/m**2\n", + "A=sqrt(I/(2*pi*n**2*p*v)) \n", + "print \"The amplitude of wave, A = %0.2e m \" %A" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The amplitude of wave, A = 5.52e-08 m \n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4, page 381" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Velocity, Amplitude of pressure and particle velocity amplitude\n", + "#given data :\n", + "gama=1.4 \n", + "P=1.013*10**5 \n", + "p1=1.29 # in kg/m**3\n", + "A=2.5*10**-7 # in m\n", + "v=sqrt(gama*P/p1) \n", + "print \"The velocity, v = %0.1f m/s \" %v\n", + "n=1000 # in Hz\n", + "lamda=v/n \n", + "print \"Wavelength, lamda = %0.4f m \" %lamda\n", + "p=p1*v*2*pi*n*A \n", + "print \"Amplitude of pressure, p = %0.2f N/m^2 \" % p\n", + "u=2*pi*n*A \n", + "print \"Particle velocity amplitude, u = %0.2e m/s \" %u" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The velocity, v = 331.6 m/s \n", + "Wavelength, lamda = 0.3316 m \n", + "Amplitude of pressure, p = 0.67 N/m^2 \n", + "Particle velocity amplitude, u = 1.57e-03 m/s \n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5, page 382" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi\n", + "# Amplitude\n", + "#given data :\n", + "v=(1/3)*10**3 # in m/s\n", + "p=1.25 # in kg/m**3\n", + "E=v**2*p \n", + "n=10**4 # in rad/sec\n", + "print \"Bulk modulus of medium, E = %0.2e N/m^2\" %E\n", + "I=10**-12 # in W/m**2\n", + "A=sqrt(I/(2*pi**2*n**2*p*v)) \n", + "print \"Amplitude of wave, A = %0.2e m \" %A\n", + "P=sqrt(2*I*p*v) \n", + "print \"Pressure amplitude, P = %0.2e N/m^2 \" %P\n", + "# answer A and E is wrong in textbook" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Bulk modulus of medium, E = 1.39e+05 N/m^2\n", + "Amplitude of wave, A = 1.10e-12 m \n", + "Pressure amplitude, P = 2.89e-05 N/m^2 \n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6, page 383" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt\n", + "# Root mean squre velocity\n", + "#given data :\n", + "vs=330 # in m/s\n", + "gama=1.41 \n", + "c=round(sqrt(3/gama)*vs) \n", + "print \"The root mean square velocity of modulus, c = %0.f m/s \"%c" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The root mean square velocity of modulus, c = 481 m/s \n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7, page 383" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Acoustic power entering\n", + "#given data :\n", + "A=1*2 # in m**2\n", + "a=80 # in dB\n", + "I0=10**-12 # in W/m**2\n", + "IbyI0=10**(80/10) \n", + "I=I0*IbyI0 \n", + "Ape=I*A \n", + "print \"Acoustic power entering the room = %0.e Watt \" %Ape" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Acoustic power entering the room = 2e-04 Watt \n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8, page 384" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import log10\n", + "# Acoustic intensity level\n", + "#given data :\n", + "Pr=3 # in W\n", + "r=15 # in m\n", + "I=Pr/(4*pi*r**2) # in W/m**2\n", + "I0=10**-12 # in W/m**2\n", + "L=round(10*log10(I/I0)) \n", + "print \"Acoustic intensity level, L = %0.f dB \" %L" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Acoustic intensity level, L = 90 dB \n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9, page 391" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# frequency\n", + "n2=200 #second**-1\n", + "l21=2 #\n", + "f=l21*n2 #\n", + "print \"Frequency = %0.f second^-1 \" %f" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Frequency = 400 second^-1 \n" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10, page 391" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# length\n", + "l1=66 #cm\n", + "v=330 #m/s\n", + "nbs=5 #beats/sec\n", + "x=(2*(v-(nbs*2*l1*10**-2))/(v*2*l1*10**-2)) #\n", + "l2=1/x #cm\n", + "print \"Length = %0.1f cm \"%(l2*100)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Length = 67.3 cm \n" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11, page 392" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# length\n", + "f=110 #Hz\n", + "v=330 #m/s\n", + "l=v/(2*f) #m\n", + "print \"Fundamental frequency = %0.f Hz\" %f\n", + "print \"Length = %0.1f m\" %l" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Fundamental frequency = 110 Hz\n", + "Length = 1.5 m\n" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12, page 392" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# equation,frequency,amplitude ,wavelength and distance\n", + "#y=6*(sin(2*pi*x)/6)*cos(160*pi*t) #given equation\n", + "a=3 #cm\n", + "T=(2*pi)/(160*pi) #sec\n", + "h=((2*pi*6)/(2*pi)) #cm\n", + "print \"wave equation is 3*sin((160*pi*t)+(2*pi*x)/6)\"\n", + "print \"Amplitude = %0.2f cm \" %a\n", + "print \"Frequency = %0.2f Hz \" %(1/T)\n", + "print h,\"wavelength is,(cm)=\"\n", + "db=h/2 #\n", + "print \"Distance between consecutive antinodes = %0.2f cm\" %db" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "wave equation is 3*sin((160*pi*t)+(2*pi*x)/6)\n", + "Amplitude = 3.00 cm \n", + "Frequency = 80.00 Hz \n", + "6.0 wavelength is,(cm)=\n", + "Distance between consecutive antinodes = 3.00 cm\n" + ] + } + ], + "prompt_number": 23 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 13, page 393" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import cos, pi\n", + "# length,amlitude,pressure\n", + "f=440 #Hz\n", + "v=330 #m/s\n", + "l=((5*v)/(4*f))*100 #cm\n", + "print \"Length, L = %0.2f cm \" %l" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Length, L = 93.75 cm \n" + ] + } + ], + "prompt_number": 27 + } + ], + "metadata": {} + } + ] +} |