Equations for Vibrations

Author: Zhiming Ou @Mattermatics Learning Center

Publisher: 3265 Public Way

ISBN: 978-997036-00-5

Summary

In reality, everything is vibrating: nothing is going on towards a certain direction definitely. Waves go back and forth; fluids flow towards every favorable direction. There is no definite equation for the vibration, everything is just on average or even by chance. In this book, I’m going to walk through the wave equations and energy diffusion equations; the purpose is to understand why and how the particles behave that way; the ultimate aim is to find a way to utilize these vibrating particles.

In physics, a wave is a disturbance or oscillation that transfers energy from one location to another through matter or space without transporting matter at all. There is a source of vibration, which cause some particles in the nearby to vibrate or move back and forth, but these particles don’t travel along with the wave itself. There are 2 types of waves: mechanical and electromagnetic. In a mechanical wave, the vibrating particles need a medium to propagate; examples include a vibrating string/membrane/rigid body, and sound. An electromagnetic wave does not a medium to propagate; it travels in vacuum with the speed of light.

There are also heat waves—the diffusion of thermal energy. The equation for heat diffusion has been solved; the behaviour of gasses is well clear. The deformation of a solid is also well described. However, behaviour of liquids is not clear yet. A solution for the Navier-Stokes Equation is not constructed yet. This is the second purpose of the book.

 

List of Content

Chapter 1 The wave theory

  • 1 Vibrating String
  • 2 Sound Waves
  • 3 Vibrating Membrane
  • 4 Body waves
  • 5 Electromagnetic Waves
  • 6 Biological waves and Brain storms

 

Chapter 2 Flow of Energy

  • 1 Heat Diffusion
  • 2 Liquids flowing
  • 3 Solid’s deformation

 

Chapter 3 Absorption of Vibration

  • 1 Refraction and Reflection of light and sound

     Fermat’s Least-Time Principle

  • 2 Standing Waves
  • 3 Wavefunctions
  • 4 How to Absorb Waves