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References: Waves: Amplitude, Frequency, Phase, and Harmonics

  1. Sine wave - Wikipedia - Defines the sine wave as the fundamental periodic shape behind y(t) = A sin(2πft + φ), the general equation this chapter builds up term by term.

  2. Harmonic - Wikipedia - Explains harmonics as integer multiples of a fundamental frequency and distinguishes them from the broader overtone category, directly supporting this chapter's fundamental-frequency-and-overtones section on timbre.

  3. Phase (waves) - Wikipedia - Covers phase as a wave's position within its own cycle relative to a reference point, the parameter this chapter uses to distinguish a sine wave from a cosine wave.

  4. The Scientist and Engineer's Guide to Digital Signal Processing - Steven W. Smith - California Technical Publishing - Smith is credited for a plain-language, formula-light treatment of sine and cosine waves and phase that avoids heavy notation, widely cited as the most accessible entry point into this exact vocabulary.

  5. Fundamentals of Musical Acoustics (2nd Revised Edition) - Arthur H. Benade - Dover Publications - Benade is credited with the clearest physical account of how a fundamental plus its overtone mixture produces timbre, illustrated with instrument-specific spectra still used as the standard teaching reference.

  6. 8.03SC Physics III: Vibrations and Waves - MIT OpenCourseWare - Full MIT course covering harmonic oscillators, periodic functions, and Fourier series, offering a deeper mathematical treatment of the wave vocabulary this chapter introduces at an intuitive level.

  7. Overtones and Harmonics - HyperPhysics - Concise reference distinguishing harmonics, which are exact integer multiples of the fundamental, from the broader category of overtones, with instrument examples matching this chapter's fundamental-and-overtones discussion.

  8. Amplitude, Time Period and Frequency of a Vibration - GeeksforGeeks - Worked-example explanation of the reciprocal relationship between period and frequency, reinforcing this chapter's T = 1/f derivation with additional practice problems and unit conversions.

  9. 1.5: More about overtones - Physics LibreTexts - Explains how harmonics arise as whole-number multiples of a fundamental frequency and how different instrument families produce different overtone spectra, directly supporting this chapter's timbre discussion.

  10. Amplitude, Period, Phase Shift and Frequency - Math Is Fun - Visual, example-driven explanation of how amplitude, frequency, and phase shift each independently affect a sine curve's graph, mirroring this chapter's parameter-by-parameter walkthrough of the general sine wave equation.