Mechanical and Electromagnetic Vibrations and Waves

Preface

Oscillatory and wave phenomena are encountered in almost all branches of physics: mechanics, geophysics, electromagnetism, optics, quantum physics, etc. Some of them were first observed in antiquity, but their scientific study only started in the 17^th Century. The phenomena include mechanical vibrations and waves, electromagnetic vibrations and waves, matter waves, etc. Electromagnetic vibrations and waves were discovered in the 19^th Century, while matter waves were discovered in the 20^th Century. Each branch of physics has its own concepts, and even its own proper mathematical language. Nevertheless, all types of vibrations and waves share several common properties: modes, similar forms of energy, superposition, interference, diffraction, etc.

The purpose of this book is to study oscillatory and wave phenomena at the undergraduate level. It was not conceived with the intended application as a textbook for a specific physics course. Some sections, indicated by an asterisk (*), may prove difficult and may be omitted without loss of continuity.

Chapter 1 introduces the basic concepts and studies some examples of vibrations of mechanical and electromagnetic systems with one or several degrees of freedom. Chapter 2 studies the superposition of vibrations and introduces Fourier analysis. Chapter 3 analyzes forced vibrations and resonances. Chapter 4 introduces the basic notions of waves in infinite media: wave equations and their solutions, energy density and energy transfer, ...