What is sound?

A short book on the physics of vibrating air.

A first-principles tour of the signal. Before any ear gets involved — before we ever invoke a cochlea, a brain, a percept — there is a disturbance in air, propagating outward from a vibrating source at the speed of sound. This volume is about that disturbance: what it is, how it moves, what mathematics governs it, and how it carries information.

The book is structured to be self-contained. We derive everything from the kinetic theory of gases up. No equation is presented without a first-principles derivation in a collapsible block alongside it. The interactives let you manipulate the constructions: ideal gases, Brownian motion, fluid slabs, Fourier sums, standing waves in tubes.

Chapters

1. Chapter 1The signalWhat sound is, before any wave equation
   1. 1.1Air at rest
   2. 1.2The kinetic-theory picture
   3. 1.3Brownian motion as fluctuation
   4. 1.4What a sound is — a small departure from equilibrium
   5. 1.5The question for the rest of the book
2. Chapter 2OscillatorsFrom simple harmonic motion to driven resonance
   1. 2.1Simple harmonic motion
   2. 2.2The complex-exponential trick
   3. 2.3Damped oscillations
   4. 2.4Driven oscillations and resonance
   5. 2.5Power, Q, and bandwidth
   6. 2.6Fourier preview — motion as a sum of sinusoids
3. Chapter 3From oscillator to waveThe string as the bridge between particles and fields
   1. 3.1A discrete chain of masses
   2. 3.2The continuum limit and the 1-D wave equation
   3. 3.3d'Alembert's solution
   4. 3.4Reflection at a boundary
   5. 3.5Standing waves and modes
4. Chapter 4The acoustic wave equationFour routes to the same equation
   1. 4.1Why four derivations?
   2. 4.2Conservation of mass for a fluid slab
   3. 4.3Euler's equation — Newton's second law in a fluid
   4. 4.4The equation of state and the adiabatic assumption
   5. 4.5Linearisation and the fluid-mechanics wave equation
   6. 4.6Route 2 — from a lattice of oscillators
   7. 4.7Route 3 — from kinetic theory and momentum flux
   8. 4.8Route 4 — from Hamilton's principle
   9. 4.9The speed of sound — same number, four meanings
5. Chapter 5Energy, momentum, impedanceWhat a sound wave actually carries
   1. 5.1Plane harmonic waves
   2. 5.2Acoustic energy density
   3. 5.3Intensity and time-averaged flux
   4. 5.4Specific acoustic impedance $\rho_0 c$
   5. 5.5The decibel, motivated
   6. 5.6Momentum carried by sound; radiation pressure
6. Chapter 6Sources and radiationWhat a vibrating object emits
   1. 6.1A pulsating sphere — the monopole
   2. 6.2Spherical waves and the inverse-square law
   3. 6.3Cylindrical waves
   4. 6.4The dipole as two opposing monopoles
   5. 6.5The piston in a baffle
7. Chapter 7Boundaries, diffraction, and modesWhat sound does when it meets something
   1. 7.1Reflection at a boundary (normal incidence)
   2. 7.2Oblique incidence and Snell for sound
   3. 7.3Transmission through a thin layer
   4. 7.4Huygens construction — one primitive, three phenomena
   5. 7.5Diffraction at an edge and through an aperture
   6. 7.6Modes of a 1-D tube
   7. 7.7Modes of a rectangular cavity
   8. 7.8Room modes and modal density
   9. 7.9Reverberation as superposition
8. Chapter 8The frequency pictureSound through the Fourier lens
   1. 8.1Sound as a spectrum — pitch, timbre, and the frequency axis
   2. 8.2Spectrograms and the time-frequency picture
   3. 8.3Acoustic filters and the room as a transfer function
   4. 8.4Resonance reborn — Q as bandwidth
9. Chapter 9Doppler and moving mediaWhen source, observer, or medium is in motion
   1. 9.1The Doppler shift — kinematic derivation
   2. 9.2The wave equation in a moving medium
   3. 9.3Source motion: subsonic, sonic, supersonic; the Mach cone
   4. 9.4Observer, source, and medium — three motions
   5. 9.5Sound from sources embedded in flow
   6. 9.6Reflection and refraction at flow boundaries
10. Chapter 10Attenuation and the nonlinear edgeWhere the small-perturbation theory breaks
    1. 10.1Viscosity and thermal absorption
    2. 10.2Molecular relaxation and atmospheric absorption
    3. 10.3The frequency dependence of attenuation
    4. 10.4When linearity breaks — wave steepening
    5. 10.5Shock formation and the second-order equations
    6. 10.6Bridge to *Cavitation*
11. Chapter GGlossaryTerms used in this book
12. Chapter BBibliographySources and further reading

Planned

More chapters are planned for this volume — deeper fluid dynamics, vibrations of strings and membranes, room acoustics in detail. The current chapter is the foundation.