Before you read this, I suggest you read post 19.14. In post 19.12, we saw how a wave could be represented, in time and space, by the wave equation. The concentration of a diffusing substance also varies in both space and time (post 18.26). Can we represent this dependence by a differential equation too? In… Continue reading 19.15 The diffusion equation

Before you read this, I suggest you read post 18.26. In post 18.26 we saw that molecules (or atoms or ions) move spontaneously from regions of high concentration to regions of low concentration, in order to increase the entropy of the system. Processes that increase entropy occur spontaneously because they lead to a more probable… Continue reading 19.14 Fick’s law of diffusion and the conduction of heat

In post 18.12 I introduced the idea of a standing wave as a vibration that could exist on a string tethered at both its ends. In the picture above, a string of length L is tethered at both ends, A and B. The fundamental wave (shown in red) then has its greatest amplitude of vibration… Continue reading 19.13 More about standing waves: intuition and analysis