Chapter 1 — The signal

What sound is, before any wave equation.

This first chapter does not write down the wave equation. Before we can derive anything we need a clear picture of what we are deriving for. Air at rest is not silent because nothing is moving — it is silent because nothing is moving coherently. Sound is what happens when a tiny coherent deviation from that bath of equilibrium chaos propagates outward.

We build the picture in five lessons:

• 1.1 Air at rest — the macroscopic equilibrium state and its three numbers (pressure, density, temperature).
• 1.2 The kinetic-theory picture — the same equilibrium from the molecular side, with a simulation.
• 1.3 Brownian motion as fluctuation — Einstein 1905; equilibrium fluctuates; the fluctuations are not sound.
• 1.4 What a sound is — the small coherent departure; the central definition for the rest of the book.
• 1.5 The question for the rest of the book — the one equation we are about to derive, four different ways.