{
"metadata": {
"name": "",
"signature": "sha256:dbcb8c7a4d852e94c64ae36b37434de99bb1000ca8d8a481769813b464811eeb"
},
"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 28 "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"#importing modules\n",
"import math\n",
"\n",
"#Variable declaration\n",
"t=0.15*10**-2; #thickness of the quartz crystal in m\n",
"Y=7.9*10**10; #young's modulus of quartz in N/m^2\n",
"rho=2650; #density of quartz in kg/m^3\n",
"\n",
"#Calculation\n",
"x=math.sqrt(Y/rho);\n",
"f=x/(2*t);\n",
"f=f*10**-6; #converting f from Hz to MHz\n",
"f=math.ceil(f*10**6)/10**6; #rounding off to 6 decimals\n",
"\n",
"#Result\n",
"print(\"fundamental frequency of vibration in MHz is\",f);\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"('fundamental frequency of vibration in MHz is', 1.819992)\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 1.2, Page number 28 "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"#importing modules\n",
"import math\n",
"\n",
"#Variable declaration\n",
"t=1e-03; #thickness of the quartz crystal in m\n",
"Y=7.9*10**10; #young's modulus of quartz in N/m^2\n",
"rho=2650; #density of quartz in kg/m^3\n",
"\n",
"#Calculation\n",
"x=math.sqrt(Y/rho);\n",
"p1=1; #for fundamental frequency p=1\n",
"f1=(p1*x)/(2*t);\n",
"F1=f1/10**6;\n",
"F1=math.ceil(F1*10**5)/10**5; #rounding off to 5 decimals\n",
"f_1=f1*10**-6; #converting f1 from Hz to MHz\n",
"f_1=math.ceil(f_1*10**5)/10**5; #rounding off to 5 decimals\n",
"p2=2; #for first overtone p=2\n",
"f2=(p2*x)/(2*t);\n",
"F2=f2/10**6;\n",
"F2=math.ceil(F2*10**5)/10**5; #rounding off to 5 decimals\n",
"f_2=f2*10**-6; #converting f2 from Hz to MHz\n",
"f_2=math.ceil(f_2*10**5)/10**5; #rounding off to 5 decimals\n",
"\n",
"#Result\n",
"print(\"fundamental frequency in Hz is\",F1,\"*10**6\");\n",
"print(\"fundamental frequency in MHz is\",f_1);\n",
"print(\"frequency of the first overtone in Hz is\",F2,\"*10**6\");\n",
"print(\"frequency of the first overtone in MHz is\",f_2);\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"('fundamental frequency in Hz is', 2.72999, '*10**6')\n",
"('fundamental frequency in MHz is', 2.72999)\n",
"('frequency of the first overtone in Hz is', 5.45998, '*10**6')\n",
"('frequency of the first overtone in MHz is', 5.45998)\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 1.3, Page number 29 "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"#importing modules\n",
"import math\n",
"\n",
"#Variable declaration\n",
"lamda=589.3*10**-9; #wavelength of light in m\n",
"f=100*10**6; #frequency of ultrasonic transducer in Hz\n",
"n=1; #order of diffraction\n",
"theta=2.25; #angle of diffraction in degrees\n",
"theta=theta*0.0174532925; #converting degrees to radians\n",
"\n",
"#Calculation\n",
"d=(n*lamda)/(2*math.sin(theta));\n",
"d1=d*10**6; #converting d from m to micro m\n",
"lamda1=2*d;\n",
"v=f*lamda1;\n",
"v=math.ceil(v*100)/100; #rounding off to 2 decimals\n",
"\n",
"#Result\n",
"print(\"wavelength of ultrasonic wave in m is\",lamda1);\n",
"print(\"velocity of ultrasonic wave in m/sec\",int(v));"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"('wavelength of ultrasonic wave in m is', 1.5010258944908707e-05)\n",
"('velocity of ultrasonic wave in m/sec', 1501)\n"
]
}
],
"prompt_number": 19
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 1.4, Page number 29 "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"#importing modules\n",
"import math\n",
"\n",
"#Variable declaration\n",
"f=2*10**6; #frequency of transducer in MHz\n",
"v=3; #speed of blood in m/s\n",
"c=800; #velocity of ultrasonic wave in m/s\n",
"theta=30; #angle of inclination in degrees\n",
"theta=theta*0.0174532925; #converting degrees to radians\n",
"\n",
"#Calculation\n",
"deltaf=(2*f*v*math.cos(theta))/c;\n",
"deltaf=deltaf*10**-6; #converting deltaf from Hz to MHz\n",
"deltaf=math.ceil(deltaf*10**6)/10**6; #rounding off to 6 decimals\n",
"\n",
"#Result\n",
"print(\"doppler shifted frequency in MHz is\",deltaf);"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"('doppler shifted frequency in MHz is', 0.012991)\n"
]
}
],
"prompt_number": 20
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 1.5, Page number 30 "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"#importing modules\n",
"import math\n",
"\n",
"#Variable declaration\n",
"Y=7.9*10**10; #young's modulus of quartz in N/m^2\n",
"rho=2650; #density of quartz in kg/m^3\n",
"\n",
"#Calculation\n",
"v=math.sqrt(Y/rho);\n",
"v=math.ceil(v*10**3)/10**3; #rounding off to 3 decimals\n",
"\n",
"#Result\n",
"print(\"velocity of ultrasonic waves in m/s is\",v);\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"('velocity of ultrasonic waves in m/s is', 5459.975)\n"
]
}
],
"prompt_number": 21
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}