#wave equation

today's gregor samsa is: in the wave equation

“The question is only whether from now on we shall have to refrain from tying description to a clear hypothesis about the real nature of the world. There are many who wish to pronounce such abdication even today. But I believe that this means making things a little too easy for oneself.”

The majority of the physical phenomena on this planet can be captured by first and second order differential equations. It is rare for a third order differential equation to show its face. Thus in according to this mathematical observation we find its correlate in the fact that we can have a wave in the water corresponding to a first-order differential equation, and a wave written on that wave corresponding to a second order differential equation. On normal shorelines one never witnesses a wave within a wave within a wave, which physical situation corresponds to a third order differential equation.

But such was the velocity of wind within the narrow channel that separates mainland Davao from Samal Island, wind so vicious it threatened to topple me over as i stood on the jetty jutting into the channel, that the water was worked up into fine wrinkles (see the upper left corner of the first photograph) , these wrinkles placed onto a wave within a wave, corresponding to that magical third order differential equation.

Water finds it difficult to fold itself more than twice, surface tension tending to smooth out wrinkles; yet here it managed to accomplish the minor marine miracle of folding itself thrice, wild wind wrinkling the waters, no other word than "wrinkle" sufficing to describe this fine liquid rumpling.

This was the first time i had seen "wrinkled water", the experience an epiphany, the wild wind bringing about the derivative of the derivative of the derivative; the wild wind allowing the water to express its existential essence more completely.

Introduction Acoustic impedance, denoted as $Z$, is a property of a medium which defines its opposition to the propagation of acoustic waves. It is a fundamental concept in fields such as acoustics, ultrasound, sonar, and other areas where sound propagation is crucial. Artistic representation of acoustic impedance as a sound wave is impeded by a central barrier. Definition of Acoustic…

Introduction The d’Alembert operator, also known as the d’Alembertian or wave operator, is a second-order differential operator that is essential in the study of wave equations in classical field theory, electromagnetism, and quantum mechanics. The d’Alembert Operator Definition The d’Alembert operator is defined in the Minkowski spacetime, the setting for the special theory of relativity. In…

Introduction The wave equation is a second-order linear partial differential equation that describes the propagation of waves—such as sound waves, light waves, and water waves—at a constant speed. It is fundamental in the fields of physics and engineering. Basic Form The basic form of the wave equation in one dimension is: $\dfrac{\partial^2 y}{\partial t^2} = v^2 \dfrac{\partial^2…

I feel like in the past couple of years I have managed to learn how not to fight the ocean I am drifting in.

I can keep my head above water without exhausting myself, sticking to movements which agree with the flow of the water and the shape of my body, not exhausting myself with contrary, desperate movements.

When I bobbed more frantically, along with the long submersions came the frantic crests, where I would pop up higher than the waves around me and catch a glimpse of the vast expanse of the landscape.

I did things, I met people, I went places. I made mistakes, I got lucky. I learned, at the price that when I landed back in the water I was guaranteed to sink again, swallowing water until I could fight my way back up.

I don’t see so far anymore. I am conserved to my patch of water, my view obscured by waves that peak and trough around me.

One of the properties of the wave equation is that you cannot extrapolate beyond its borders. I cannot infer about the wider world from my experience, nor do I have the flashes of knowledge that I did before, knowledge that is aging rapidly.

But there is much to learn about my patch of water. Now that I have control of my movement, I can begin to look around. I can see the fish swim by, and identify the brush of kelp. I can begin to notice the patterns that shift to and fro.