Physics of Music is a one-semester course in how musical sound is produced, transmitted, and perceived. It takes a single thread, something vibrates, the vibration travels as a wave, the wave is heard, and follows it from a mass on a spring through to a digital recording, stopping wherever music has something to ask of physics.
The subject has an unusual advantage as a physics course: the reader already has decades of data. Everyone knows what a violin sounds like, that a large room rings and a small one does not, that a choir singing in tune is different from a choir nearly in tune. The physics does not have to argue that these effects exist. It has to explain them, and the explanations are unusually satisfying because the prediction can be checked by listening.
Audience and prerequisites¶
The intended reader is a university student of any major, taking this as a science course. The mathematics required is algebra, trigonometry, and logarithms: if the phrase “solve for ” and the sine function are familiar, that is enough. Calculus is not required and is not used in the main argument. Where a result is genuinely a calculus result: the wave equation from Newton’s second law, Fourier coefficients as integrals, the Bessel functions that describe a drumhead: the derivation is placed in a clearly marked dropdown, stated as optional, and never depended on afterward. A reader who has had calculus will find those dropdowns are where the book stops taking their word for it; a reader who has not can skip every one and lose nothing.
No musical training is assumed. Staff notation appears only where it is the clearest picture available, and it is explained where it is first used. Readers who want a fuller treatment of the musical side will find the companion volumes Understanding Music Theory and Open Music Theory in the same series; this book cross-references them rather than duplicating them.
Instructors will find the chapters sized for assignment by numbered section. A fifteen-week pacing guide is in the Teaching Guide.
Organization¶
The book has six parts.
Part I, Sound and Vibration establishes the physical vocabulary: simple harmonic motion, the wave that carries a vibration through air, superposition and interference, and the standing waves and resonances that let an object have a pitch at all.
Part II, Spectrum and Timbre is the hinge of the book. Fourier’s result, that any periodic sound is a sum of harmonics, is what connects the shape of an instrument to the character of its sound, and almost every later chapter uses it.
Part III, Hearing and Perception turns from the sound to the listener: the mechanics of the ear, why loudness is not intensity, why pitch is not frequency, and where consonance comes from.
Part IV, Scales and Tuning takes up the oldest quantitative problem in music. Small whole-number ratios sound good and do not fit into an octave; every tuning system in history is a different answer to that arithmetic.
Part V, Musical Instruments works through the families, strings, winds, percussion, and the voice, asking of each the same three questions: what vibrates, what sets it going, and what couples it to the air.
Part VI, Sound in Space and in Circuits follows the sound after it leaves the instrument, into the room that shapes it and the microphone that captures it.
How the chapters are built¶
Every chapter opens with learning objectives and a short introduction, then proceeds through numbered reading sections (§N.1, §N.2, …) kept roughly equal in length so an assignment can be stated as a range of sections. Worked examples are embedded in the reading, not quarantined at the end. Each chapter closes with a summary, a set of conceptual questions, and a problem set. Every problem opens with a tag, Straightforward, Moderate, or Challenging, marking how much it asks beyond a direct application of the chapter’s formulas, useful when assigning a subset, or when deciding which one to try first. Solutions to every problem are included in the complete edition and omitted from the student edition.
A handful of pedagogical asides appear where they earn their keep: notes for historical context, tips for problem-solving strategy, warnings for common misconceptions, and margin remarks for a unit or a term that would otherwise interrupt the sentence. Dropdowns hold the optional derivations described above. None of these is a substitute for the main argument; all can be ignored on a first reading.
Audio examples run throughout the book. Each appears as a figure showing the waveform and spectrum of the clip, a sentence describing what is heard, and a link to hear it. They are synthesized rather than recorded, which is a deliberate limitation: a synthesized clip can isolate exactly one variable, the same pitch and the same level, differing only in which harmonics are present, in a way no recording of a real instrument can. Because every example carries its picture and its description, they work equally in print and for readers who cannot hear them. Where the real thing matters, the text says so and sends the reader to an instrument.
Interactive simulations from PhET and OpenLyceum are embedded wherever a moving picture teaches more than a static one. In the print and Word editions the same figures appear as screenshots, each caption linking to the running simulation.
The laboratory and the project¶
Two appendices exist because two of the course’s aims cannot be met by reading. Laboratory Exercises is a set of measurements using an oscilloscope, a function generator, and audio-analysis software, or the browser simulations that stand in for all three where the hardware is missing, enough to take the book’s claims about spectra, air columns, and beats and check them. The Final Project is guidance for measuring something of one’s own and explaining it to somebody who does not know any physics, which is harder than it sounds and is the skill most likely to outlast the course.
A note on what is left out¶
This is a physics book about music, not a music book with physics in it. It has little to say about why a particular piece is beautiful, and it should not be read as claiming that the physics explains the music. What the physics explains is the medium: the constraints every instrument maker, tuner, singer, and hall designer has had to work within, and the reasons those constraints are what they are. Musicians solved most of these problems by ear, centuries before anyone could write down why the solutions worked. Part of the pleasure of the subject is discovering how often they were exactly right.