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-{
- "metadata": {
- "name": "",
- "signature": "sha256:f155f4255421e223741f26abb6caa1287b63505ee5f432c40968d5b5ff6fb505"
- },
- "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",
- "#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",
- "#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",
- "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": {}
- }
- ]
-} \ No newline at end of file
generated by cgit (git 2.34.1) at 2025-01-08 20:12:21 +0000