A sound’s time-domain rate of change determines its frequency-domain bandwidth

Evidence

This argument can be reversed to show that when the output of an acoustic system, such as a musical instrument, changes slowly, its spectrum occupies a narrow bandwidth, whereas when it changes quickly, it must occupy a larger bandwidth. This can be due to an increase in the number of harmonics present in the spectrum, as would be the case if the waveform becomes sharper or more spiky. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 489

Categorization

• XREF: The time-frequency uncertainty principle here parallels quantum mechanics’ position-momentum uncertainty; also builds the conceptual foundation for why impulsive attacks need broadband spectra. — connects to: Rapid changes in a sound’s amplitude envelope force broader spectral bandwidth — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 489; Fast-changing acoustic signals necessarily occupy a wider spectral bandwidth. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 489; How fast a sound changes dictates how wide its spectral bandwidth must be. — David Howard, Jamie Angus, coustics and Psychoacoustics, 487 (+2 more)

Broader Connections

• Rapid changes in a sound’s amplitude envelope force broader spectral bandwidth #corroborates (0.95) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 489
• Fast-changing acoustic signals necessarily occupy a wider spectral bandwidth. #corroborates (0.95) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 489
• How fast a sound changes dictates how wide its spectral bandwidth must be. #corroborates (0.95) — David Howard, Jamie Angus, coustics and Psychoacoustics, 487
• Noise envelope fluctuation rate is inversely proportional to bandwidth #exemplifies (0.85) — Professor Dr.-Ing. Hugo Fastl, Professor Dr.-Ing. Eberhard, Psychoacoustics- Facts and Models, 87
• Shorter sounds necessarily have broader spectral bandwidths #expands (0.80) — Jennifer Lentz, Psychoacoustics- Perception of Normal…, 177