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diff --git a/Applied_Physics-I_by_I_A_Shaikh/Chapter4.ipynb b/Applied_Physics-I_by_I_A_Shaikh/Chapter4.ipynb new file mode 100755 index 00000000..ded2d042 --- /dev/null +++ b/Applied_Physics-I_by_I_A_Shaikh/Chapter4.ipynb @@ -0,0 +1,1309 @@ +{ + "metadata": { + "celltoolbar": "Raw Cell Format", + "name": "", + "signature": "sha256:c8b4bc6a0f384361dda4e7989c0d96facf075884a24ed18090bbb83730c8fbed" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 4: Acoustics and Ultrasonics" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.11.1,Page number 4-17" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given data\n", + "d=8900.0 #density\n", + "Y=20.8*10**10 #Young's modulus\n", + "n=40*10**3 #frequency of wave\n", + "k=1.0 #consider 1st harmonic\n", + "\n", + "l=(k/(2*n))*math.sqrt(Y/d) #arranging formula of natural frequency\n", + "\n", + "print\"length =\",round(l,4),\"meter\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "length = 0.0604 meter\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.12.1,Page number 4-20" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given data\n", + "\n", + "d=2.65*10**3 #density\n", + "Y=8*10**10 #Young's modulus\n", + "n=1*10**6 #frequency of wave\n", + "k=1.0 #consider 1st harmonic\n", + "\n", + "t=(k/(2*n))*sqrt(Y/d) #arranging formula of natural frequency\n", + "\n", + "print\"thickness =\",round(t,4),\"meter\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "thickness = 0.0027 meter\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.1,Page number 4-25" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data\n", + "l=20 #length of room\n", + "b=15 #bredth of room\n", + "h=10 #height of room\n", + "V=l*b*h #volume of room\n", + "a=0.106 #absorption coefficient\n", + "\n", + "S=2*(l*b+b*h+h*l) #surface area of hall\n", + "\n", + "T=(0.161*V)/(a*S) #Reverberation time,using Sabine's formula\n", + "\n", + "print\"Reverberation time =\",round(T,4),\"sec\"\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Reverberation time = 3.5051 sec\n" + ] + } + ], + "prompt_number": 20 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.2,Page number 4-26" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "m=1j #original sound intensity\n", + "n=1000*1j #increased intensity value\n", + "\n", + "l=10*log10(n/m) #change in intensity level\n", + "\n", + "print\"change in intensity level =\",l,\"dB\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "change in intensity level = (30+0j) dB\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.3,Page number 4-26" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "S1=220 #wall area\n", + "a1=0.03 #absorption coefficient for the wall\n", + "S2=120 #floor area\n", + "a2=0.8 #absorption coefficient for the floor\n", + "S3=120 #ceiling area\n", + "a3=0.06 #absorption coefficient for the ceiling\n", + "V=600 #volume of room\n", + "\n", + "S=S1+S2+S3 #total surface area\n", + "\n", + "a=(a1*S1+a2*S2+a3*S3)/S #average sound absorption coefficient\n", + "\n", + "print\"1) average sound absorption coefficient =\",round(a,4)\n", + "\n", + "T=(0.161*V)/(a*S) #Reverberation time,using Sabine's formula\n", + "\n", + "print\"2) Reverberation time =\",round(T,4),\"sec\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) average sound absorption coefficient = 0.2387\n", + "2) Reverberation time = 0.8798 sec\n" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.4,Page number 4-27" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given data\n", + "\n", + "V=5500 #volume\n", + "T=2.3 #Reverberation time\n", + "S=750 #sound absorption coefficient\n", + "a=(0.161*V)/(S*T) #using Sabine's formula\n", + "\n", + "print\"average absorption coefficient =\",round(a,4)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "average absorption coefficient = 0.5133\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.5,Page number 4-27" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "l=20 #length of room\n", + "b=12 #bredth of room\n", + "h=12 #height of room\n", + "V=l*b*h #volume of room\n", + "S=2*(l*b+b*h+h*l) #surface area of hall\n", + "T1=2.5 #Reverberation time\n", + "\n", + "a=(0.161*V)/(T1*S) #using Sabine's formula\n", + "\n", + "print\"1) average absorption coefficient =\",round(a,4)\n", + "\n", + "a1=0.5 #absorption coefficient\n", + "T2=2 #Reverberation time\n", + "\n", + "S1=(0.161*V/(a1-a))*(1.0/T2-1.0/T1)\n", + "\n", + "print\"2) carpet area required =\",round(S1,4),\"m^2\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) average absorption coefficient = 0.1486\n", + "2) carpet area required = 131.958 m^2\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.6,Page number 4-28" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "Ac=10*12 #area of carpet covering entire floor\n", + "ac=0.06 #absorption coefficient of carpet\n", + "\n", + "aS1=Ac*ac #absorption due to carpet\n", + "\n", + "Af=10*12 #area of false celling\n", + "af=0.03 #absorption coefficient of celling\n", + "\n", + "aS2=Af*af #absorption due to celling\n", + "\n", + "As=100*1 #area of cushioned sets\n", + "a_cush=1 #absorption coefficient of cushion sets\n", + "\n", + "aS3=As*a_cush #absorption due to cusion sets\n", + "\n", + "Aw=346*1 #area of walls covered with absorbent\n", + "aw=0.2 #absorption coefficient of walls\n", + "\n", + "aS4=Aw*aw #absorption due to walls\n", + "\n", + "Ad=346*1 #area of wooden door\n", + "ad=0.2 #absorption coefficient of wooden door\n", + "\n", + "aS5=Ad*ad #absorption due to wooden door\n", + "\n", + "aS=aS1+aS2+aS3+aS4 #total absorption\n", + "\n", + "ap=0.46 #absorption coefficient of audience/person\n", + "l=12 #assuming length of wall\n", + "b=10 #assuming breadth of wall\n", + "h=8 #assuming height of wall\n", + "\n", + "V=l*b*h #volume of hall\n", + "\n", + "#case 1 :(no one inside/emptey hall)\n", + "\n", + "T1=(0.161*V)/aS #reverberation time\n", + "\n", + "print\" 1)reverberation time of empty hall =\",round(T1,4),\"sec\"\n", + "\n", + "#case 2 :(50 person inside hall)\n", + "\n", + "T2=(0.161*V)/(aS+50*0.46) #reverberation time\n", + "\n", + "print\" 2)reverberation time of hall with 50 person =\",round(T2,4),\"sec\"\n", + "\n", + "#case 2 :(100 person inside hall/full capacity of hall)\n", + "\n", + "T3=(0.161*V)/(aS+100*0.46) #reverberation time\n", + "\n", + "print\" 3)reverberation time of hall with 100 person =\",round(T3,4),\"sec\"\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " 1)reverberation time of empty hall = 0.8587 sec\n", + " 2)reverberation time of hall with 50 person = 0.7614 sec\n", + " 3)reverberation time of hall with 100 person = 0.6839 sec\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.7,Page number 4-30" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "l=20 #length of room\n", + "b=15 #bredth of room\n", + "h=5 #height of room\n", + "\n", + "V=l*b*h #volume of room\n", + "S=2*(l*b+b*h+h*l) #surface area of hall\n", + "\n", + "T=3.5 #Reverberation time\n", + "\n", + "a=(0.161*V)/(T*S) #using Sabine's formula\n", + "\n", + "print\"1) average absorption coefficient =\",round(a,4)\n", + "\n", + "avg=a*S #average total absorption\n", + "\n", + "print\"2) average total absorption =\",round(avg,4),\"m^2.s\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) average absorption coefficient = 0.0726\n", + "2) average total absorption = 69.0 m^2.s\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.8,Page number 4-30" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "l=20 #length of room\n", + "b=15 #bredth of room\n", + "h=10 #height of room\n", + "\n", + "V=l*b*h #volume of room\n", + "\n", + "a=0.1 #absorption coefficient\n", + "\n", + "S=2*(l*b+b*h+h*l) #surface area of hall\n", + "\n", + "T1=(0.161*V)/(a*S) #Reverberation time,using Sabine's formula\n", + "\n", + "print\"1) Reverberation time =\",round(T1,4),\"sec\"\n", + "\n", + "a2=0.66 #absorption coefficient of curtain cloth\n", + "\n", + "S2=100 #surface area of a curtain cloth\n", + "\n", + "T2=(0.161*V)/(a*S+a2*S2*2) #Reverberation time,using Sabine's formula\n", + "\n", + "T=T1-T2 #change in Reverberation time\n", + "\n", + "print\"2) change in Reverberation time =\",round(T,4),\"sec\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) Reverberation time = 3.7154 sec\n", + "2) change in Reverberation time = 1.8719 sec\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.9,Page number 4-30" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "S1=220 #wall area\n", + "a1=0.03 #absorption coefficient for the wall\n", + "S2=120 #floor area\n", + "a2=0.8 #absorption coefficient for the floor\n", + "S3=120 #ceiling area\n", + "a3=0.06 #absorption coefficient for the ceiling\n", + "V=600 #volume of room\n", + "\n", + "S=S1+S2+S3 #total surface area\n", + "a=(a1*S1+a2*S2+a3*S3)/S #average sound absorption coefficient\n", + "\n", + "print\"1) average sound absorption coefficient =\",round(a,4)\n", + "\n", + "T=(0.161*V)/(a*S) #Reverberation time,using Sabine's formula\n", + "\n", + "print\"2) Reverberation time =\",round(T,4),\"sec\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) average sound absorption coefficient = 0.2387\n", + "2) Reverberation time = 0.8798 sec\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.10,Page number 4-31" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "f=0.07*10**6 #frequency\n", + "t=0.65 #time\n", + "v=1700 #velocity of sound\n", + "\n", + "d=v*t/2 #depth of seabed\n", + "\n", + "print\"1) depth of seabed =\",round(d,4),\"meter\"\n", + "\n", + "lamda=v/f #wavelength\n", + "\n", + "print\"2) wavelength =\",round(lamda,4),\"meter\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) depth of seabed = 552.5 meter\n", + "2) wavelength = 0.0243 meter\n" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.11,Page number 4-31" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "t=1*10**-3 #thicknesss of crystal\n", + "d=2.65*10**3 #density\n", + "Y=8*10**10 #Young's modulus\n", + "k=1 #consider 1st harmonic\n", + "\n", + "n=(k/(2*t))*sqrt(Y/d) #formula of natural frequency\n", + "\n", + "print\" natural frequency =\",\"{0:.3e}\".format(n),\"Hz\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " natural frequency = 2.747e+06 Hz\n" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.12,Page number 4-32" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "d=2650 #density\n", + "Y=8*10**10 #Young's modulus\n", + "k=1.0 #consider 1st harmonic\n", + "\n", + "#case 1\n", + "\n", + "n1=3.8*10**6 #frequency of wave\n", + "\n", + "t1=(k/(2*n1))*sqrt(Y/d) #arranging formula of natural frequency\n", + "\n", + "print\"1) thickness =\",\"{0:.3e}\".format(t1),\"meter\"\n", + "\n", + "#case 2\n", + "\n", + "n2=300*10**3 #frequency of wave\n", + "\n", + "t2=(k/(2*n2))*sqrt(Y/d) #arranging formula of natural frequency\n", + "\n", + "print\"2) thickness =\",\"{0:.3e}\".format(t2),\"meter\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) thickness = 7.230e-04 meter\n", + "2) thickness = 9.157e-03 meter\n" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.13,Page number 4-32" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "d=2650 #density\n", + "Y=8*10**10 #Young's modulus\n", + "n=2*10**6 #frequency of wave\n", + "k=1.0 #consider 1st harmonic\n", + "\n", + "t=(k/(2*n))*sqrt(Y/d) #arranging formula of natural frequency\n", + "\n", + "print\"thickness =\",\"{0:.3e}\".format(t),\"meter\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "thickness = 1.374e-03 meter\n" + ] + } + ], + "prompt_number": 25 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.14,Page number 4-33" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "f=50*10**3 #frequency\n", + "v1=348 #velocity of ultrasound in atmosphere\n", + "v2=1392 #velocity of ultrasound in sea water\n", + "t=2.0 #time difference\n", + "\n", + "#distance is constant hence v1*t1=v2*t2\n", + "\n", + "m=v2/v1 #assuming constant as m\n", + "\n", + "#(t1-t2=d) and (t1=m*t2) therefore\n", + "\n", + "t2=t/(m-1)\n", + "\n", + "d=v2*t2 #distance between two ship\n", + "\n", + "print\"distance between two ships =\",round(d,4),\"meter\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "distance between two ships = 928.0 meter\n" + ] + } + ], + "prompt_number": 27 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.15,Page number 4-34" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#for case1\n", + "t1=2*10**-3 #thicknesss of plate\n", + "d=2.65*10**3 #density\n", + "Y=8*10**10 #Young's modulus\n", + "k=1.0 #consider 1st harmonic\n", + "\n", + "n1=(k/(2*t1))*sqrt(Y/d) #formula of natural frequency\n", + "\n", + "print\"1)natural frequency =\",\"{0:.3e}\".format(n1),\"Hz\"\n", + "\n", + "#for case2\n", + "\n", + "n2=3*10**6 #frequency\n", + "\n", + "t2=(k/(2*n2))*sqrt(Y/d) #arranging formula of natural frequency\n", + "\n", + "t=t1-t2 #change in thickness\n", + "\n", + "print\"2)change in thickness =\",\"{0:.3e}\".format(t),\"meter\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1)natural frequency = 1.374e+06 Hz\n", + "2)change in thickness = 1.084e-03 meter\n" + ] + } + ], + "prompt_number": 29 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.16,Page number 4-34" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "S=10 #salinity\n", + "t=2 #time\n", + "T=20 #temperature\n", + "\n", + "v=1510+1.14*S+4.21*T-0.037*T**2 #velocity of ultrasound in sea\n", + "\n", + "d=v*t/2 #depth of sea bed\n", + "\n", + "print\"depth of sea bed =\",round(d,4),\"meter\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "depth of sea bed = 1590.8 meter\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.17,Page number 4-35" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "S=29 #salinity\n", + "t=2 #time\n", + "l=0.01 #wavelength\n", + "T=30 #temperature\n", + "\n", + "v=1510+1.14*S+4.21*T-0.037*T**2 #velocity of ultrasound in sea\n", + "\n", + "d=v*t/2 #depth of sea bed\n", + "\n", + "print\"1)depth of sea bed =\",round(d,4),\"meter\"\n", + "\n", + "f=v/l #frequency\n", + "\n", + "print\"2) frequency =\",\"{0:.3e}\".format(f),\"Hz\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1)depth of sea bed = 1636.06 meter\n", + "2) frequency = 1.636e+05 Hz\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.18,Page number 4-35" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "v1=5.9*10**3 #velocity of UW in mild steel\n", + "v2=4.3*10**3 #velocity of UW in brass\n", + "t2=15*10**-3 #thickness of brass plate\n", + "\n", + "t1=v2*t2/v1 #since ve;ocity is inversly proportional to thickness\n", + "\n", + "print\"real thickness =\",\"{0:.3e}\".format(t1),\"meter\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "real thickness = 1.093e-02 meter\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.19,Page number 4-36" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "t1=4*10**-3 #thickness of 1st crystal\n", + "n1=400*10**3 #frequency of 1st crystal\n", + "n2=500*10**3 #frequency of 2nd crystal\n", + "\n", + "t2=n1*t1/n2 #since frquency is inversly proportional to thickness\n", + "\n", + "print\"thickness of 2nd crystal =\",\"{0:.3e}\".format(t2),\"meter\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "thickness of 2nd crystal = 3.200e-03 meter\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.20,Page number 4-36" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "t2=30*10**-6 #pulse arrival time of defective steel bar\n", + "t1=80*10**-6 #pulse arrival time of non defective steel bar\n", + "d=40*10**-2 #bar thickness\n", + "\n", + "x=(t2/t1)*d\n", + "\n", + "print\"distance at which defect has occurred =\",round(x,4),\"meter\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "distance at which defect has occurred = 0.15 meter\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.21,Page number 4-37" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "d=18*10**-3 #thickness\n", + "v=5.9*10**3 #velocity\n", + "\n", + "t=(2*d)/v #echo time\n", + "\n", + "print\"echo time =\",\"{0:.3e}\".format(t),\"sec\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "echo time = 6.102e-06 sec\n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.22,Page number 4-37" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "t=1*10**-3 #thickness of quartz crystal\n", + "\n", + "#given t=l/2\n", + "\n", + "l=t*2 #wavelength\n", + "Y=7.9*10**10 #young's module of crystal\n", + "p=2650 #density of crystal\n", + "\n", + "v=sqrt(Y/p) #velocity of vibration\n", + "\n", + "n=v/l #frequency of vibration\n", + "\n", + "print\"frquency of vibration =\",\"{0:.3e}\".format(n),\"Hz\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "frquency of vibration = 2.730e+06 Hz\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.23,Page number 4-38" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "#given data\n", + "\n", + "d=7.23*10**3 #density\n", + "Y=11.6*10**10 #Young's modulus\n", + "n=20*10**3 #frequency of wave\n", + "k=1.0 #consider 1st harmonic\n", + "\n", + "l=(k/(2*n))*sqrt(Y/d) #arranging formula of natural frequency\n", + "\n", + "print\"length =\",\"{0:.3e}\".format(l),\"meter\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "length = 1.001e-01 meter\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.24,Page number 4-38" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#for case1\n", + "t1=2*10**-3 #thicknesss of plate\n", + "d=2.65*10**3 #density\n", + "Y=8*10**10 #Young's modulus\n", + "k=1.0 #consider 1st harmonic\n", + "\n", + "n1=(k/(2*t1))*sqrt(Y/d) #formula of natural frequency\n", + "\n", + "print\"1)natural frequency =\",\"{0:.3e}\".format(n1),\"Hz\"\n", + "\n", + "#for case2\n", + "\n", + "n2=3*10**6 #frequency\n", + "\n", + "t2=(k/(2*n2))*sqrt(Y/d) #arranging formula of natural frequency\n", + "\n", + "t=t1-t2 #change in thickness\n", + "\n", + "print\"2)change in thickness =\",\"{0:.3e}\".format(t),\"meter\"\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1)natural frequency = 1.374e+06 Hz\n", + "2)change in thickness = 1.084e-03 meter\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.25,Page number 4-39" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "l=20 #length of room\n", + "b=15 #bredth of room\n", + "h=10 #height of room\n", + "\n", + "V=l*b*h #volume of room\n", + "S=2*(l*b+b*h+h*l) #surface area of hall\n", + "\n", + "T=3 #Reverberation time\n", + "\n", + "a=(0.161*V)/(T*S) #using Sabine's formula\n", + "\n", + "print\"1) average absorption coefficient =\",round(a,4)\n", + "\n", + "m=a*S #total absorption\n", + "\n", + "print\"2) total absorption of surface =\",round(m,4),\"m**2/sec\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) average absorption coefficient = 0.1238\n", + "2) total absorption of surface = 161.0 m**2/sec\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.26,Page number 4-39" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "#for case1\n", + "t1=1.8*10**-3 #thicknesss of plate\n", + "d=2.65*10**3 #density\n", + "Y=8*10**10 #Young's modulus\n", + "k=1.0 #consider 1st harmonic\n", + "\n", + "n1=(k/(2*t1))*sqrt(Y/d) #formula of natural frequency\n", + "\n", + "print\"1)natural frequency =\",\"{0:.3e}\".format(n1),\"Hz\"\n", + "\n", + "#for case2\n", + "\n", + "n2=2*10**6 #frequency\n", + "\n", + "t2=(k/(2*n2))*sqrt(Y/d) #arranging formula of natural frequency\n", + "\n", + "t=t1-t2 #change in thickness\n", + "\n", + "print\"2)change in thickness =\",\"{0:.3e}\".format(t),\"meter\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1)natural frequency = 1.526e+06 Hz\n", + "2)change in thickness = 4.264e-04 meter\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15.27,Page number 4-39" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "n=0.4999*10**6 #frequency\n", + "t=5.5*10**-3 #thicknesss of plate\n", + "d=2.65*10**3 #density\n", + "k=1.0 #consider 1st harmonic\n", + "\n", + "Y=4*(t**2)*(n**2)*d/k #arranging formula of natural frequency\n", + "\n", + "print\"Youngs modulus =\",\"{0:.3e}\".format(Y),\"N/m**2\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Youngs modulus = 8.013e+10 N/m**2\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +}
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