UltrasoUnd Physics & instrUmentation - Pegasus Lectures
UltrasoUnd Physics & instrUmentation - Pegasus Lectures UltrasoUnd Physics & instrUmentation - Pegasus Lectures
11. Distance Equation ..................................................................................................................................33 11.1 Exercises: Distance Equation ......................................................................................................34 12. Math Terminology .................................................................................................................................35 12.1 The Language of Mathematics: Translating English into Mathematics ......................................35 12.2 Mathematical Definition ..............................................................................................................35 12.3 Exercises: Math Terminology ......................................................................................................37 13. Distance Equation Revisited .................................................................................................................39 13.1 The Roundtrip Effect ...................................................................................................................39 13.2 When the Propagation Velocity of 1540 m/sec is Incorrect ........................................................41 13.3 Exercises: Distance Equation Revisited ......................................................................................42 14. Non-Linear Relationships ......................................................................................................................43 14.1 Direct Non-Linear Proportionality ..............................................................................................43 14.2 Complex - Inverse Proportionality ..............................................................................................44 15. Interpreting Relationships Within Linear and Non-Linear Equations ...................................................44 15.1 Assessing an Equation and Expressing the Relative Relationship ..............................................44 15.2 Exercises: Assessing an Equation ................................................................................................46 15.3 Exercises: Proportionality............................................................................................................47 16. Dealing with Percentage Change ...........................................................................................................48 16.1 Simple Calculations with Proportional Variables ........................................................................48 16.2 Calculations with Non-linearly Related Variables .......................................................................49 16.3 Rules for Dealing with Percentage Change .................................................................................49 16.4 Examples .....................................................................................................................................49 17. Logarithms .............................................................................................................................................51 17.1 Properties of Logarithms .............................................................................................................52 17.2 Exercises: Logarithms .................................................................................................................53 18. Trigonometry..........................................................................................................................................53 18.1 Angles, Quadrants and Signs .......................................................................................................57 18.2 The Value of Knowing Basic Trigonometry in Ultrasound (and Medicine) ...............................58 18.3 Exercises: Trigonometry ..............................................................................................................59 19. The Decimal System and the Binary System .........................................................................................61 19.1 Decimal (Base 10) and Binary (Base 2) ......................................................................................61 19.2 Exercises: Decimal Conversions .................................................................................................62 19.3 Binary ..........................................................................................................................................62 19.4 Converting from Binary to Base 10 .............................................................................................63 19.5 Converting from Decimal to Binary ............................................................................................64 19.6 Exercises: Binary .........................................................................................................................65 20. Analog to Digital (A/D) Conversion .....................................................................................................66 21. Nyquist Criteria .....................................................................................................................................71 22. Addition of Waves .................................................................................................................................76 22.1 Constructive Interference (In Phase Waves) ................................................................................76 22.2 Destructive Interference (Out of Phase Waves) ...........................................................................77 22.3 Partial Constructive (or Partially Destructive) Interference ........................................................77 CHaPTeR 2 - Waves Introduction ..................................................................................................................................................81 1. The Motivation for Studying Waves .....................................................................................................81 2. Waves ....................................................................................................................................................81 2.1 Definition of a Wave ....................................................................................................................81 2.2 Examples of Waves ......................................................................................................................82 xiv Pegasus Lectures, Inc.
3. Classification of Waves .........................................................................................................................82 3.1 Benefit to Classifications .............................................................................................................82 3.2 Electromagnetic (EM) Waves ......................................................................................................83 3.3 Mechanical Waves .......................................................................................................................83 4. Conceptual Questions ............................................................................................................................84 5. Propagation of Mechanical Waves ........................................................................................................84 5.1 Transverse Waves ........................................................................................................................84 5.2 Longitudinal Waves .....................................................................................................................85 5.2.1 Definition and Depiction ................................................................................................85 5.2.2 Developing a More Thorough Understanding of Longitudinal Waves ..........................86 5.3 Problems with Static Drawings of Waves ...................................................................................86 6. Variations in the Medium with Propagation (Acoustic Variables) ........................................................88 6.1 Pressure ........................................................................................................................................88 6.2 Density .........................................................................................................................................89 6.2.1 The Equation for Density ..............................................................................................89 6.2.2 Density as an Acoustic Variable .....................................................................................89 6.3 Temperature .................................................................................................................................89 6.3.1 Generation of Heat ........................................................................................................89 6.3.2 Measuring Temperature .................................................................................................90 6.4 Particle Motion ...........................................................................................................................90 7. Conceptual Questions ............................................................................................................................90 8. Wave Characteristics and Parameters ....................................................................................................92 8.1 General.........................................................................................................................................92 8.2 Four Basic Parameters and the Many Associated Parameters .....................................................92 8.3 Frequency (f) and Period (P) .......................................................................................................93 8.3.1 General ...........................................................................................................................93 8.3.2 Frequency of a Sound Wave ..........................................................................................93 8.3.3 Graphical Depiction of Frequency .................................................................................93 8.3.4 Determining the Frequency ...........................................................................................94 8.3.5 The Relationship Between Time (Period) and Frequency .............................................94 8.3.6 Interpreting the Period ...................................................................................................95 8.4 Propagation Velocity ....................................................................................................................96 8.4.1 Defining Speed and Velocity ..........................................................................................96 8.4.2 Units and Graphical Representation ..............................................................................96 8.4.3 What Determines the Speed of Sound ...........................................................................96 8.4.4 Graphical Depiction of Propagation Speed for Sound Waves .......................................97 8.5 Wavelength ..................................................................................................................................98 8.5.1 Definition .......................................................................................................................98 8.5.2 Graphical Representation ...............................................................................................99 8.5.3 Distinguishing the Wavelength from the Period ............................................................99 8.5.4 What Determines the Wavelength................................................................................100 8.5.5 The Wavelength Equation ............................................................................................101 8.5.6 Different Ways of Remembering the Wavelength Equation ........................................101 8.6 Amplitude ..................................................................................................................................102 8.6.1 Definition .....................................................................................................................102 8.6.2 Units .............................................................................................................................102 8.6.3 Graphical Representation .............................................................................................102 8.6.4 Calculating the Amplitude ...........................................................................................103 9. Conceptual Questions ..........................................................................................................................105 Pegasus Lectures, Inc. xv Table of Contents
- Page 1 and 2: Frank r. miele, msee President, Peg
- Page 3 and 4: dedication This book is dedicated t
- Page 5: thank yoU to the FolloWinG imaGe co
- Page 8 and 9: keypoints: The keypoints serve as a
- Page 10 and 11: medium Printed text CD objectives U
- Page 12 and 13: This independent learning education
- Page 16 and 17: 10. Exercises .....................
- Page 18 and 19: 9.2.2 Examples of Scattering in the
- Page 20 and 21: CHaPTeR 5 - Transducers Introductio
- Page 22 and 23: 2.3 Signals, Noise, and Signal-to-N
- Page 24 and 25: 19.2 Purposes for Cine Review .....
- Page 26 and 27: VolUMe 2 CHaPTeR 7 - Doppler Introd
- Page 28 and 29: 22.4 Color Display and Velocity Int
- Page 30 and 31: 8.3 Transmit Voltages for Various M
- Page 32 and 33: 1.2 Commitment to Quality .........
- Page 34 and 35: 1. Removing Some of the Simplificat
- Page 36 and 37: 1.2 Power .........................
- Page 38 and 39: 10.3 Pressure Volume Loop .........
- Page 40 and 41: To learn the basics of ultrasound (
- Page 42 and 43: 42 Note: Children generally learn t
- Page 44: Additionally, all fractions can be
11. Distance Equation ..................................................................................................................................33<br />
11.1 Exercises: Distance Equation ......................................................................................................34<br />
12. Math Terminology .................................................................................................................................35<br />
12.1 The Language of Mathematics: Translating English into Mathematics ......................................35<br />
12.2 Mathematical Definition ..............................................................................................................35<br />
12.3 Exercises: Math Terminology ......................................................................................................37<br />
13. Distance Equation Revisited .................................................................................................................39<br />
13.1 The Roundtrip Effect ...................................................................................................................39<br />
13.2 When the Propagation Velocity of 1540 m/sec is Incorrect ........................................................41<br />
13.3 Exercises: Distance Equation Revisited ......................................................................................42<br />
14. Non-Linear Relationships ......................................................................................................................43<br />
14.1 Direct Non-Linear Proportionality ..............................................................................................43<br />
14.2 Complex - Inverse Proportionality ..............................................................................................44<br />
15. Interpreting Relationships Within Linear and Non-Linear Equations ...................................................44<br />
15.1 Assessing an Equation and Expressing the Relative Relationship ..............................................44<br />
15.2 Exercises: Assessing an Equation ................................................................................................46<br />
15.3 Exercises: Proportionality............................................................................................................47<br />
16. Dealing with Percentage Change ...........................................................................................................48<br />
16.1 Simple Calculations with Proportional Variables ........................................................................48<br />
16.2 Calculations with Non-linearly Related Variables .......................................................................49<br />
16.3 Rules for Dealing with Percentage Change .................................................................................49<br />
16.4 Examples .....................................................................................................................................49<br />
17. Logarithms .............................................................................................................................................51<br />
17.1 Properties of Logarithms .............................................................................................................52<br />
17.2 Exercises: Logarithms .................................................................................................................53<br />
18. Trigonometry..........................................................................................................................................53<br />
18.1 Angles, Quadrants and Signs .......................................................................................................57<br />
18.2 The Value of Knowing Basic Trigonometry in Ultrasound (and Medicine) ...............................58<br />
18.3 Exercises: Trigonometry ..............................................................................................................59<br />
19. The Decimal System and the Binary System .........................................................................................61<br />
19.1 Decimal (Base 10) and Binary (Base 2) ......................................................................................61<br />
19.2 Exercises: Decimal Conversions .................................................................................................62<br />
19.3 Binary ..........................................................................................................................................62<br />
19.4 Converting from Binary to Base 10 .............................................................................................63<br />
19.5 Converting from Decimal to Binary ............................................................................................64<br />
19.6 Exercises: Binary .........................................................................................................................65<br />
20. Analog to Digital (A/D) Conversion .....................................................................................................66<br />
21. Nyquist Criteria .....................................................................................................................................71<br />
22. Addition of Waves .................................................................................................................................76<br />
22.1 Constructive Interference (In Phase Waves) ................................................................................76<br />
22.2 Destructive Interference (Out of Phase Waves) ...........................................................................77<br />
22.3 Partial Constructive (or Partially Destructive) Interference ........................................................77<br />
CHaPTeR 2 - Waves<br />
Introduction ..................................................................................................................................................81<br />
1. The Motivation for Studying Waves .....................................................................................................81<br />
2. Waves ....................................................................................................................................................81<br />
2.1 Definition of a Wave ....................................................................................................................81<br />
2.2 Examples of Waves ......................................................................................................................82<br />
xiv<br />
<strong>Pegasus</strong> <strong>Lectures</strong>, Inc.
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