## Archive for February, 2007

### LaTeX now native on WordPress

2007 February 17

Now that WordPress has $\LaTeX$, let’s play around a little… I can’t call myself a “musical naturalist” without showing you the equations that describe the propagation of sound and music. Behold… the acoustic wave equation and the principles from which it derives:

Conservation of Mass

$\dfrac{d\rho}{dt} + \rho (\vec{\nabla} \cdot \vec{v}) = 0$

Conservation of Momentum

$\rho \dfrac{d\vec{v}}{dt} = - \vec{\nabla} P$

Conservation of Energy

$\rho \dfrac{dU}{dt} - \dfrac{P}{\rho} \dfrac{d\rho}{dt} = 0$

Equation of State:

$\dfrac{\partial P}{\partial t} + \vec{v}\cdot\vec{\nabla}P = c^2 \left(\dfrac{\partial \rho}{\partial t}+\vec{v}\cdot\vec{\nabla}\rho\right)$

$P \sim c^2 \rho$

Acoustic Wave Equation:

$\nabla^2 P - \dfrac{1}{c^2}\dfrac{\partial^2 P}{\partial t^2} = 0$

Simplify by assume time-dependence of form $e^{i\omega t}$:

$P(\vec{x},t) \propto P(\vec{x})e^{i\omega t}$

Helmholtz Equation

$\nabla^2 P + k^2 P = 0$ with $k^2 = \dfrac{\omega^2}{c^2}$

Solution #1: No boundaries, homogeniuos, isotropic media (spherical coordinates) in the limit $|kr|>>1$

$P(r) \sim P_{0}\dfrac{e^{ikr}}{kr}$

### Introduction

2007 February 12

Lately, I’ve been trying out various tools for dumping ideas and bits of usefully organized information into easily accesible places such as this. The GOTO factor is just so unbelievably useful. As in “Hey, friend… have you seen [insert blob]? No? Well, just check out my site at [insert Web 2.0 tool]”.

I really got hooked on del.icio.us, but need a place to dump my own content too. I was convinced by the ridiculously charming host of geekbrief.tv to take a spin with WordPress. When I saw that it was GPL, I had no choice but to strike a blow for democracy and try out another open-source tool.

Much of what will be posted here will be of no interest to the vast majority of the intelligent life in this universe, nor should I think to those in any other. I hope you find some of what lands on this site useful and/or amusing.

### Hello world!

2007 February 10

This is a test. This is only a test. In the event that this had been a actual blog, you’d be greeted with a witty story with regards to what this is all about. As a substitute, I offer you only this mindless rambling. Enjoy!