Links to related material and teachers' resources (some pages still under construction). Phasor addition Phasor representation of Simple Harmonic Motion. Adding phasors with different amplitudes and phase but equal frequency. Constructive and destructive interference. What if frequencies are different? Phasor and Lissajous representations compared. Tartini tones, consonance, temperament, harmony and scales. Examples of Tartini tones for consonant intervals. Tuning with Tartini tones. Just intonation. Modulation and temperament. Equal temperament. Other temperaments. Harmony and scales. Interference beats and Tartini tones Interference beats between two sine waves. Algebraic and graphical derivations. Sample audio files with oscillograms and spectra. Tuning using beats. Consonance -> beats -> roughness -> separate notes. Consonant intervals. Linear and non-linear superposition  Linear and non-linear superposition of two sine waves using circuits with resistors and a diode. Sample audio files with oscillograms and spectra. Lissajous figures Explanation of the laboratory setup used for Lissajous figures, interference beats and Tartini tones. Sample audio files with Lissajous figures, oscillograms and spectra. Laboratories on Sound and Waves Downloadable phase locked oscillators. Mechanical resonances: cantilever, pendulums linear and nonlinear, mass and spring, Chladni patterns. Travelling waves: stretched string, spring, water waves. Reflection and transmission at discontinuities. Sound pressure vs distance from source. Doppler experiments: bicycles, running, circular motion. Chladni patterns Explanation of vibratory modes, nodes and antinodes. Movie clips recording the transitions between modes for a variety of Chladni patterns.

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