I wrote about exponential growth and decay in posts 16.5 and 16.6; I want to return to this topic again to introduce some ideas that I will use in later posts. Let’s invent a number called e (it was really invented by Jacob Bernoulli in 1683); we will define it raised to the power x… Continue reading 18.15 More about exponential growth: the number e

Before you read this, I suggest you read posts 18.10, 18.11 and 18.12. The picture above shows waves on the sea. Their shape is much more complicated than the simple sine and cosines waves (see picture below) that I have used to represent waves in previous posts (like post 18.10). Can we use the ideas… Continue reading 18.14 Wave shapes – Fourier series

When an object moves in air, it must push the air away from it; it changes the motion of the air and, by definition, so exerts a force on it (post 16.13). Since pressure is simply force divided by the area on which it acts (post 17.5), the object increases the pressure in the direction… Continue reading 18.13 Sound