Fundamental Physics of Ultrasound
eBook - ePub

Fundamental Physics of Ultrasound

  1. 394 pages
  2. English
  3. ePUB (mobile friendly)
  4. Available on iOS & Android
eBook - ePub

Fundamental Physics of Ultrasound

About this book

Based on lectures by the author, this volume is designed as a textbook on general ultrasonics. The text provides coverage of the propagation of ultrasonic waves in media with different elastic properties and under conditions close to those encountered in scientific and practical applications of ultrasound.

Frequently asked questions

Yes, you can cancel anytime from the Subscription tab in your account settings on the Perlego website. Your subscription will stay active until the end of your current billing period. Learn how to cancel your subscription.
At the moment all of our mobile-responsive ePub books are available to download via the app. Most of our PDFs are also available to download and we're working on making the final remaining ones downloadable now. Learn more here.
Perlego offers two plans: Essential and Complete
  • Essential is ideal for learners and professionals who enjoy exploring a wide range of subjects. Access the Essential Library with 800,000+ trusted titles and best-sellers across business, personal growth, and the humanities. Includes unlimited reading time and Standard Read Aloud voice.
  • Complete: Perfect for advanced learners and researchers needing full, unrestricted access. Unlock 1.4M+ books across hundreds of subjects, including academic and specialized titles. The Complete Plan also includes advanced features like Premium Read Aloud and Research Assistant.
Both plans are available with monthly, semester, or annual billing cycles.
We are an online textbook subscription service, where you can get access to an entire online library for less than the price of a single book per month. With over 1 million books across 1000+ topics, we’ve got you covered! Learn more here.
Look out for the read-aloud symbol on your next book to see if you can listen to it. The read-aloud tool reads text aloud for you, highlighting the text as it is being read. You can pause it, speed it up and slow it down. Learn more here.
Yes! You can use the Perlego app on both iOS or Android devices to read anytime, anywhere — even offline. Perfect for commutes or when you’re on the go.
Please note we cannot support devices running on iOS 13 and Android 7 or earlier. Learn more about using the app.
Yes, you can access Fundamental Physics of Ultrasound by Shutilov,Vladimir Alexandrovich Shutilov,Yelena Vladimirovna Tcharnaya in PDF and/or ePUB format, as well as other popular books in Technology & Engineering & Civil Engineering. We have over one million books available in our catalogue for you to explore.

XI. Propagation of Ultrasound in Crystals

§ 1. General acoustic equations for crystals

A crystal is an anisotropic medium, so that its equation of motion in the linear approximation must be expressed in the general form (I.11). The stress σjk can be expressed in the same approximation in terms of the strain with the help of relation (I.13c) :
σik=ciklj∊lj,XI.1
in which the elastic moduli ciklj must be written with four indices (i, k, l, j = 1, 2, 3). Since, according to the definition (I.2), ∊lj = (1/2)(δu/δxl + δul/δxj) for small deformations, the substitution of relation (XI.1) into the equation of motion (I.11) reduces the latter to an equation for one unknown — the displacement vector:
ρ0∂2ui∂t2=-ciklj(∂2uj∂xk∂xl+∂2ul∂xk∂xj).XI.2
If in the expression cikljδ2ul/δxkδxj we interchange the dummy indices l and j, we obtain cikjl, δ2uj/δxkδxl The tensor cikjl, however, is symmetric relative to the second pair of indices; both terms in parentheses in Eq. (XI.2) are therefore equal and the equations of motion for the components of the displacement vector u assume the form
ρ0∂2ui∂t2=ciklj ∂2uj∂xk∂xl.XI.3
This expression, as before, contains three equations for the components of ...

Table of contents

  1. Cover
  2. Half Title
  3. Title Page
  4. Copyright Page
  5. Table of Contents
  6. Foreword to the English Edition
  7. Preface
  8. List of Symbols
  9. I. Basic Equations of the Theory of Elasticity
  10. II. Propagation of Ultrasonic Waves in Liquids and Gases
  11. III. Sinusoidal Plane Waves with Infinitesimal Amplitude
  12. IV. Finite-Amplitude Plane Waves
  13. V. Steady Forces Arising in an Ultrasonic Field
  14. VI. Ultrasonic Cavitation
  15. VII. Reflection, Refraction and Scattering of Ultrasonic Waves
  16. VIII. Transmission of Plane Waves Through Layers. Electro Acoustical Analogies. Radiation of Plane Waves
  17. IX. Spherical Waves
  18. X. Propagation of Ultrasound in an Isotropic Solid
  19. XI. Propagation of Ultrasound in Crystals
  20. Problems
  21. Solutions
  22. References
  23. Bibliography
  24. Subject Index