There are all sorts of resonances around us, in the world, in our culture, and in our technology. A tidal resonance causes the 55 foot tides in the Bay of Fundy. Mechanical and acoustical resonances and their control are at the center of practically every musical instrument that ever existed. Even our voices and speech are based on controlling the resonances in our throat and mouth. Technology is also a heavy user of resonance. All clocks, radios, televisions, and gps navigating systems use electronic resonators at their very core. Doctors use magnetic resonance imaging or MRI to sense the resonances in atomic nuclei to map the insides of their patients. In spite of the great diversity of resonators, they all share many common properties. In this blog, we will delve into their various aspects. It is hoped that this will serve both the students and professionals who would like to understand more about resonators. I hope all will enjoy the animations.

Friday, January 12, 2007

The Author

The author is a retired professor of both physics and electrical engineering. After receiving his Ph.D. from Stanford in physics, he taught electromagnetic fields and elementary labs at George Mason University, in Fairfax, Virginia for 30 years. He was one of the originators of thermoacoustics (engines and refrigerators using acoustics instead of pistons) and has done research in superconducting microwave resonators, electron beam microwave amplifiers, worked with a startup company Microwave Technology, Inc, and worked on the roots of quantum mechanics. He has long felt that computer animation could aid in the teaching of waves and fields.

If you google on Ceperley you may notice the great volume of hits on D.M. Ceperley, a brother, who is also a physicist and is at the University of Illinois.

Amazon	new and used text books	iPods & MP3 players	cell phones & service
computers	flat-panel TV's	ear phones	movies

My favorite reference books on waves:

Waves, Berkeley Physics Course - vol. 3, Frank S. Crawford, Jr. McGraw-Hill 1965. This book is suitable for an add-on to an introductory course on college or university physics. It discusses all sorts of aspects of waves and has a multitude of home experiments. One could probably make a great science fair project from one of them. As to its math level, it mostly uses algebra, with some calculus in the mix.

Physics of waves, by Elmore and Heald, originally published by McGraw-Hill in 1969, but currently published by Dover. This book covers many different wave systems, such as waves on a string, on a membrane, in solids, in fluids, on a liquid surface, and electromagnetic waves. It also covers the many aspects of waves. It has an excellent chapter on diffraction.

The Feynman lectures on physics, Feynman, Leighton, and Sands, Addison-Wesley 1963. Three volumes. These cover many aspects of physics. They are perhaps best suited for someone who has made it through an introductory sequence in college or university physics, and wants to read about the subject from a more sophisticated point of view. They are not particularly math intensive, more just into discussing concepts with some math as required. These are books you read to understand a physicist's mind. Perhaps 10% to 20% of the chapters are about waves and resonances.

Electromagnetic books that I use:

Engineering Electromagnetics, Hayt (with Buck on more recent editions), McGraw-Hill. An easy to read, compact junior-level text for electrical engineering students.

Fields and waves in communication electronics, Ramo, Whinnery, Van Duzer, Wiley. A upper level/graduate level text for electrical engineering student. Covers practically every aspect of applied electromagnetic fields in some depth. Is not a book to sit down and read for philosophy, but rather to look up the rational behind certain devices or design methods.

Resonances, Waves, and Fields Contents
Wave-centric interpretation of quantum mechanics Three types of waves Mathematical expressions for one dimensional traveling waves Standing waves in one dimension Waves in a ring resonator - standing and rotating waves Traveling and standing waves in two and three dimensions - Cartesian coordinates Standing waves and rotating waves in two dimensional circular resonators Standing waves and rotating waves in three dimensional cylindrical resonators Spherical harmonics The Lagrangian approach to simple waves - several common waves that lack momentum Why only J’s in a standard Bessel expansion? Games with arrays of wave emitters Octave programs used in emitter games Brunelleschis Dome - its structure and construction Origins of Newton's laws of motion Conformal mapping - solving Laplace's equation Contents of conformal mapping postings Introduction to conformal mapping Conformal mapping II Fluid flow patterns handled by other functions Conformal mapping of electric and magnetic fields Detailed conformal mappings Simple resonators, shock excitation Introduction - various examples Shock excitation Complex math derivation Strong damping - critical damping How a resonator works Energy in a resonator Power loss in resonators Energy and power by complex methods Valid method of multiplying two complex phasors Modulation, an application of phasor multiplication Up/down conversion, an application of phasor multiplication Q, quality factor Resonators - continuous excitation Sinusoidal excitation of a resonator - contents Damping Driven oscillations Various looks of resonance curves Resonance peak properties The resonance peak - qualitatively More on the impact model Mathematical response to a very short impulse Summing impulses with calculus Buildup and decay of envelope Supplemental derivation Q - a review and more Coupling of waves to a resonator Coupling strength Waveguide excited resonator with circulator Resonant scattering of waves - one dimensional cases Circuit analysis of the acoustical circuit in Fig. 35 Electrical model of the acoustical circuit in Fig. 35 of posting 3.15 Looking at the resonator part of the circuit Steady state response of the circuit: transmission line, coupling inductor and resonator Transmission line resonators Steady state response of a transmission line resonator via a Smith Chart Differential equation solution for transient response and SPICE simulation Summary of analysis of a transmission line excited resonator using a circulator Circuit analysis of resonant scattering with two output channels Separating out the radiated and simply reflected components - mathematical Applying methods of 3.18 to the circuit of 3.17 Derivation of wave properties for transmission lines Reflection and absorption coefficients for transmission lines with loads Comparison of series and parallel LRC resonant circuits Clocks History of Mechanical Clocks with Animations: Understanding a mechanical clock with animations: includes pendulum, balance wheel and quartz clocks Index for resonances, waves and fields Album of 24 flash animations showing the physics of oscillations, waves, and phasors The LRC circuit, the classical simple resonator: Marconi invents the wireless telegraph. Use of complex numbers in oscillations and waves: Euler's formula and complex numbers: an introduction to and history of complex numbers. Details on infinite series. The technology of oscillations and waves demand new mathematical methods: a look at the mathematical difficulty of dealing with oscillations and waves. Phasors More on complex numbers: to prepare for using them for oscillations and waves. Complex phasors The algebra of complex phasors True waves Waves using complex phasors Types of waves Superposition and standing waves Complex phasor representation of a standing wave Reflection of waves as a process to make standing waves Water Waves: Water waves Water waves - mathematical derivation - part 1 Water waves derivation 2 - dynamics of the free surface Fourier Analysis: The spectrum of a waveform - Fourier Analysis Mathematical definition of Fourier series Sines, cosines, and phases How good is a Fourier series of a function at reproducing the original function? Symmetries in Fourier series Special relativity Non-mathematical introduction to relativity - 9 part series - NEW - Mathematics of special relativity - 19 part series Programming in swishMax and flash: Matrix manipulation routines for swishMax Ways to make Waves: programming and non-programming methods for animating waves in swishMax and flash. The Author Permitted use of material on this blog and how to download free animations from this site. Index for resonances, waves and fields