{
"metadata": {
"name": "",
"signature": "sha256:e55f587b2da98ead68f73bb2b4d29bef91aa67eb577c460fb9dcaab92acc4339"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Ultrasonics"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 1.1, Page number 20"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#To calculate the depth of a submerged submarine\n",
"\n",
"#Variable declaration\n",
"v = 1440; #velocity of ultrasonic waves(m/s)\n",
"t = 0.33; #time elapsed(s)\n",
"\n",
"#Calculation\n",
"d = v*t; #distance travelled(m)\n",
"d1 = d/2; #depth of submarine(m)\n",
"\n",
"#Result\n",
"print \"depth of the submerged submarine is\",d1, \"m\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"depth of the submerged submarine is 237.6 m\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 1.2, Page number 21"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#To calculate the natural frequency \n",
"\n",
"#importing modules\n",
"import math\n",
"\n",
"#Variable declaration\n",
"l = 40; #length of iron rod(mm)\n",
"E = 115*10**9; #Young's modulus(N/m**2)\n",
"rho = 7.25*10**3; #density of pure iron(kg/m**3)\n",
"\n",
"#Calculation\n",
"l = l*10**-3; #length of iron rod(m)\n",
"new = (1/(2*l))*math.sqrt(E/rho); #natural frequency of the rod(Hz)\n",
"new = new*10**-3; #natural frequency of the rod(kHz)\n",
"new=math.ceil(new*10**3)/10**3; #rounding off to 3 decimals\n",
"\n",
"#Result\n",
"print \"depth of the submerged submarine is\",new, \"kHz\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"depth of the submerged submarine is 49.785 kHz\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 1.3, Page number 21"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#To calculate the fundamental frequency \n",
"\n",
"#importing modules\n",
"import math\n",
"\n",
"#Variable declaration\n",
"l = 1; #length of quartz crystal(mm)\n",
"E = 7.9*10**10; #Young's modulus(N/m**2)\n",
"rho = 2650; #density(kg/m**3)\n",
"\n",
"#Calculation\n",
"l = l*10**-3; #length of iron rod(m)\n",
"new = (1/(2*l))*math.sqrt(E/rho); #natural frequency of the rod(Hz)\n",
"new = new*10**-6; \n",
"new=math.ceil(new*10**2)/10**2; #rounding off to 2 decimals\n",
"\n",
"#Result\n",
"print \"fundamental frequency of crystal is\",new, \"*10**6 Hz\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"fundamental frequency of crystal is 2.73 *10**6 Hz\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 1.4, Page number 22"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#To calculate the velocity of waves\n",
"\n",
"#importing modules\n",
"import math\n",
"\n",
"#Variable declaration\n",
"d = 0.55; #distance between 2 constructive antinodes(mm)\n",
"new = 1.5; #frequency of crystal(MHz)\n",
" \n",
"#Calculation\n",
"new = new*10**6; #frequency of crystal(Hz)\n",
"d = d*10**-3; #distance between 2 constructive antinodes(m)\n",
"#distance between 2 antinodes is given by lamda/2\n",
"lamda = 2*d; #wavelength of ultrasonic waves(m)\n",
"v = new*lamda; #velocity of waves(m/s)\n",
"\n",
"#Result\n",
"print \"velocity of waves is\",int(v), \"m/s\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"velocity of waves is 1650 m/s\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 1.5, Page number 22"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#To calculate the natural frequency\n",
"\n",
"#importing modules\n",
"import math\n",
"\n",
"#Variable declaration\n",
"l = 50; #length of rod(mm)\n",
"E = 11.5*10**10; #Young's modulus(N/m**2)\n",
"rho = 7250; #density(kg/m**3)\n",
"\n",
"#Calculation\n",
"l = l*10**-3; #length of iron rod(m)\n",
"new = (1/(2*l))*math.sqrt(E/rho); #natural frequency of the rod(Hz)\n",
"new = new*10**-3; #natural frequency of the rod(kHz)\n",
"new = math.ceil(new*10**2)/10**2; #rounding off to 2 decimals\n",
"\n",
"#Result\n",
"print \"natural frequency of rod is\",new, \"kHz\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"natural frequency of rod is 39.83 kHz\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 1.6, Page number 22"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#To calculate the frequency\n",
"\n",
"#importing modules\n",
"import math\n",
"\n",
"#Variable declaration\n",
"l = 2; #length of crystal(mm)\n",
"E = 7.9*10**10; #Young's modulus(N/m**2)\n",
"rho = 2650; #density(kg/m**3)\n",
"\n",
"#Calculation\n",
"l = l*10**-3; #length of iron rod(m)\n",
"new = (1/(2*l))*math.sqrt(E/rho); #natural frequency of the rod(Hz)\n",
"new = new*10**-6; #natural frequency of the rod(MHz)\n",
"new=math.ceil(new*10**3)/10**3; #rounding off to 3 decimals\n",
"\n",
"#Result\n",
"print \"frequency of crystal is\",new, \"MHz\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"frequency of crystal is 1.365 MHz\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 1.7, Page number 23"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#To calculate the frequency\n",
"\n",
"#importing modules\n",
"import math\n",
"\n",
"#Variable declaration\n",
"l = 3; #length of crystal(mm)\n",
"E = 8*10**10; #Young's modulus(N/m**2)\n",
"rho = 2500; #density(kg/m**3)\n",
"\n",
"#Calculation\n",
"l = l*10**-3; #length of iron rod(m)\n",
"new = (1/(2*l))*math.sqrt(E/rho); #natural frequency of the rod(Hz)\n",
"new = new*10**-3; #natural frequency of the rod(kHz) \n",
"new=math.ceil(new*10**2)/10**2; #rounding off to 2 decimals\n",
"\n",
"#Result\n",
"print \"frequency of crystal is\",new, \"kHz\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"frequency of crystal is 942.81 kHz\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 1.8, Page number 23"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#To calculate the frequency\n",
"\n",
"#importing modules\n",
"import math\n",
"\n",
"#Variable declaration\n",
"l = 1.5; #length of crystal(mm)\n",
"E = 7.9*10**10; #Young's modulus(N/m**2)\n",
"rho = 2650; #density(kg/m**3)\n",
"\n",
"#Calculation\n",
"l = l*10**-3; #length of iron rod(m)\n",
"new = (1/(2*l))*math.sqrt(E/rho); #natural frequency of the rod(Hz)\n",
"new = new*10**-6; #natural frequency of the rod(MHz) \n",
"new=math.ceil(new*10**2)/10**2; #rounding off to 2 decimals\n",
"\n",
"#Result\n",
"print \"frequency of crystal is\",new, \"MHz\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"frequency of crystal is 1.82 MHz\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 1.9, Page number 24"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#To calculate the depth of the sea\n",
"\n",
"#Variable declaration\n",
"v = 1440; #velocity of ultrasonic waves(m/s)\n",
"t = 0.95; #time elapsed(s)\n",
"\n",
"#Calculation\n",
"d = v*t; #distance travelled(m)\n",
"d1 = d/2; #depth of sea(m)\n",
"\n",
"#Result\n",
"print \"depth of the submerged submarine is\",int(d1), \"m\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"depth of the submerged submarine is 684 m\n"
]
}
],
"prompt_number": 10
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 1.10, Page number 24"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#To calculate the depth of a submerged submarine\n",
"\n",
"#Variable declaration\n",
"v = 1440; #velocity of ultrasonic waves(m/s)\n",
"t = 0.83; #time elapsed(s)\n",
"\n",
"#Calculation\n",
"d = v*t; #distance travelled(m)\n",
"d1 = d/2; #depth of submarine(m)\n",
"\n",
"#Result\n",
"print \"depth of the submerged submarine is\",d1, \"m\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"depth of the submerged submarine is 597.6 m\n"
]
}
],
"prompt_number": 11
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 1.11, Page number 24"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#To calculate the reverberation time of hall\n",
"\n",
"#importing modules\n",
"import math\n",
"\n",
"#Variable declaration\n",
"aS = 1050; #total absorption inside hall(Sabine)\n",
"V = 9000; #volume of cinema hall(m**3)\n",
"\n",
"#Calculation\n",
"T = 0.165*V/aS; #reverberation time of hall(s)\n",
"T = math.ceil(T*10**4)/10**4; #rounding off to 4 decimals\n",
"\n",
"#Result\n",
"print \"reverberation time of the hall is\",T, \"s\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"reverberation time of the hall is 1.4143 s\n"
]
}
],
"prompt_number": 13
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 1.12, Page number 25"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#To calculate the area of interior surface\n",
"\n",
"#importing modules\n",
"import math\n",
"\n",
"#Variable declaration\n",
"a = 0.65; #average absorption coefficient(Sabine/m**2)\n",
"V = 13500; #volume of auditorium(m**3)\n",
"T = 1.2; #reverberation time of hall(s)\n",
"\n",
"#Calculation\n",
"S = 0.165*V/(a*T); #reverberation time of hall(s)\n",
"S = math.ceil(S*10)/10; #rounding off to 1 decimal\n",
"\n",
"#Result\n",
"print \"total area of interior surface is\",S, \"m**2\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"total area of interior surface is 2855.8 m**2\n"
]
}
],
"prompt_number": 14
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 1.13, Page number 25"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#To calculate the new reverberation time of hall\n",
"\n",
"#importing modules\n",
"import math\n",
"\n",
"#Variable declaration\n",
"V = 15000; #volume of cinema hall(m**3)\n",
"T1 = 1.3; #initial reverberation time of hall(s)\n",
"a1S1 = 300; #number of chairs placed\n",
"\n",
"#Calculation\n",
"aS = 0.165*V/T1; #total absorption of hall\n",
"T2 = (0.165*V)/(aS+a1S1); #reverberation time of hall after adding chairs(s)\n",
"T2 = math.ceil(T2*10**4)/10**4; #rounding off to 4 decimals\n",
"\n",
"#Result\n",
"print \"reverberation time of the hall after adding chairs is\",T2, \"s\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"reverberation time of the hall after adding chairs is 1.1231 s\n"
]
}
],
"prompt_number": 16
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 1.14, Page number 26"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#To calculate the depth of a submerged submarine\n",
"\n",
"#Variable declaration\n",
"v = 1440; #velocity of ultrasonic waves(m/s)\n",
"t = 0.5; #time elapsed(s)\n",
"\n",
"#Calculation\n",
"d = v*t; #distance travelled(m)\n",
"d1 = d/2; #depth of submarine(m)\n",
"\n",
"#Result\n",
"print \"depth of the submerged submarine is\",int(d1), \"m\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"depth of the submerged submarine is 360 m\n"
]
}
],
"prompt_number": 17
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 1.15, Page number 26"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#To calculate the velocity of waves\n",
"\n",
"#importing modules\n",
"import math\n",
"\n",
"#Variable declaration\n",
"d = 0.4; #distance between 2 constructive antinodes(mm)\n",
"new = 1.5; #frequency of crystal(MHz)\n",
" \n",
"#Calculation\n",
"new = new*10**6; #frequency of crystal(Hz)\n",
"d = d*10**-3; #distance between 2 constructive antinodes(m)\n",
"#distance between 2 antinodes is given by lamda/2\n",
"lamda = 2*d; #wavelength of ultrasonic waves(m)\n",
"v = new*lamda; #velocity of waves(m/s)\n",
"\n",
"#Result\n",
"print \"velocity of waves is\",int(v), \"m/s\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"velocity of waves is 1200 m/s\n"
]
}
],
"prompt_number": 18
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 1.16, Page number 26"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#To calculate the natural frequency \n",
"\n",
"#importing modules\n",
"import math\n",
"\n",
"#Variable declaration\n",
"l = 40; #length of iron rod(mm)\n",
"E = 11.5*10**10; #Young's modulus(N/m**2)\n",
"rho = 7250; #density of pure iron(kg/m**3)\n",
"\n",
"#Calculation\n",
"l = l*10**-3; #length of iron rod(m)\n",
"new = (1/(2*l))*math.sqrt(E/rho); #natural frequency of the rod(Hz)\n",
"new = new*10**-3; #natural frequency of the rod(kHz)\n",
"new=math.ceil(new*10**3)/10**3; #rounding off to 3 decimals\n",
"\n",
"#Result\n",
"print \"depth of the submerged submarine is\",new, \"kHz\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"depth of the submerged submarine is 49.785 kHz\n"
]
}
],
"prompt_number": 19
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}