Wave and particle models of sound are complementary, not competing

Sound can be modeled as a continuous wave (Fourier analysis, spectral synthesis) or as a stream of discrete particles (granular synthesis). These views are not opposed but complementary, just as wave and particle theories in quantum physics are complementary. Fourier analysis excels at revealing steady-state spectral content; granular decomposition excels at representing transient and time-varying phenomena. The Gabor matrix integrates both views: it is a time-frequency representation that decomposes sound into elementary quanta (particles with both time and frequency locality). A practitioner chooses the model best suited to the task rather than treating one as ‘correct.‘

Examples

A pitched organ tone is well-described by its harmonic wave spectrum. A thunderclap is better described as a burst of noise particles scattered in time.

Assessment

In what situations is the particle model of sound more useful than the wave model? Give a concrete synthesis or transformation scenario for each.