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{
"metadata": {
"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 8: Ultrasonics"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.1, Page 429"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"d = 8e-004; # Thickness of the piece of piezoelectric crystal, m\n",
"v = 5760; # Velocity of ultrasonic waves in the piece of piezoelectric crystal, m/s\n",
"\n",
"#Calculations\n",
"n = v/(2*d); # The frequency of the fundamental mode of ultrasonic wave, Hz\n",
"\n",
"#Result\n",
"print \"The frequency of the fundamental mode of ultrasonic wave = %3.1f MHz\"%(n/1e+006)\n",
"\n",
" "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The frequency of the fundamental mode of ultrasonic wave = 3.6 MHz\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.2, Page 430"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import *\n",
"\n",
"#Variable declaration\n",
"d = 2e-003; # Thickness of the piece of quarts crystal, m\n",
"rho = 2650; # Density of the crystal, kg/meter-cube\n",
"Y = 7.9e+010; # Value of Youngs Modulus, N/metre-square\n",
"\n",
"#Calculations\n",
"n = 1/(2*d)*sqrt(Y/rho); #The frequency of the fundamental mode of vibration, Hz\n",
"\n",
"#Result\n",
"print \"The frequency of the fundamental mode of vibration in quatrz crystal = %5.3f Hz\"%(n/1e+006)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The frequency of the fundamental mode of vibration in quatrz crystal = 1.365 Hz\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.3, Page 430"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"v = 5e+003; # Velocity of ultrasonic beam in steel plate, m/s\n",
"n = 25e+003; # Difference between two neighbouring harmonic frequencies (Nm - Nm_minus1), Hz \n",
"\n",
"#Calculations\n",
"d = v/(2*n); # The thickness of steel plate, m\n",
"\n",
"#Result\n",
"print \"The thickness of steel plate = %3.1f m\"%d\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The thickness of steel plate = 0.1 m\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.4, Page 430"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import *\n",
"\n",
"#Variable declaration\n",
"n = 1e+006; # Frequency of Ultrasonic waves, Hz \n",
"C = 2.5e-014; # Capcitance of capacitor, F\n",
"\n",
"#Calculations\n",
"# Frequency of elecric oscillations is given by n = 1/(2*%pi)*sqrt(1/(L*C)), solving for L\n",
"L = 1/(4*pi**2*n**2*C); # The inductance of an inductor to produce ultrasonic waves, henry\n",
"\n",
"#Result\n",
"print \"The inductance of an inductor to produce ultrasonic waves = %d henry\"%L\n",
"\n",
" "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The inductance of an inductor to produce ultrasonic waves = 1 henry\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.5, Page 431"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"d = 50e-002; # Thickness of the metallic rod, m\n",
"t1 = 30e-006; # Arrival time for first pulse, s\n",
"t2 = 80e-006; # Arrival time for second pulse, s\n",
"\n",
"#Calculations&Results\n",
"v = 2*d/t2; # Velocity of ultrasonic waves, m/s\n",
"print \"The velocity of pulse inside the rod = %4.2e m/s\"%v\n",
"x = t1*v/2;\n",
"print \"The position of pulse inside the rod = %6.4f m\"%x\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The velocity of pulse inside the rod = 1.25e+04 m/s\n",
"The position of pulse inside the rod = 0.1875 m\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.6, Page 431"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import *\n",
"\n",
"#Variable declaration\n",
"I = 2.5e+004; # Sound intensity, W/meter-square\n",
"v = 1480; # Sound velocity, m/s\n",
"rho_w = 1000; # Density of water, kg/meter-cube\n",
"rho_c = 2650; # Density of crystal of transducer, kg/meter-cube\n",
"d = 0.001; # Thickness of the quartz, m\n",
"f = 20e+003; # Frequency of sound in water, Hz\n",
"\n",
"#Calculations&Results\n",
"# As sound intensity, I = p^2/(2*rho1*v), solving for p\n",
"p = sqrt(2*rho_w*v*I); # Pressure in the medium, N/metre-square\n",
"a = p/(d*rho_c); # Maximum acceleration of the quartz ultrasonic transducer, metre/second-square\n",
"print \"The maximum acceleration produced in quartz transducer = %4.2e metre/second-square\"%a\n",
"y = a/(2*pi*f)**2; # Maximum displacement of the quartz transducer, m\n",
"print \"The maximum displacement of quartz transducer = %3.1f micrometer\"%(y/1e-006)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The maximum acceleration produced in quartz transducer = 1.03e+05 metre/second-square\n",
"The maximum displacement of quartz transducer = 6.5 micrometer\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.7, Page 432"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"L = 0.2; # Length of a magnetostrictive hydrophone, m\n",
"lamda = 2*L; # Wavelength of ultrasonic wave, m\n",
"v = 4900; # Velocity of ultrasonic beam in water, m/s\n",
"\n",
"#Calculations\n",
"f = v/lamda; # Fundamental frequency of ultrasonic, KHz\n",
"\n",
"#Result\n",
"print \"The fundamental frequency of a magnetostrictive hydrophone = %4.2f KHz\"%(f/1e+03)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The fundamental frequency of a magnetostrictive hydrophone = 12.25 KHz\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.8, Page 432"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"v = 3700; # Velocity of ultrasonic beam in copper, m/s\n",
"t = 1e-006; # Delay time for ultrasonic beam, s\n",
"\n",
"#Calculations\n",
"L = v*t; # # Length of a copper wire required for a delay, m\n",
"\n",
"#Result\n",
"print \"The length of a copper wire required for a delay = %6.4f m\"%L\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The length of a copper wire required for a delay = 0.0037 m\n"
]
}
],
"prompt_number": 10
}
],
"metadata": {}
}
]
}
|
