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{
"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": {}
}
]
}
|
