Faster sound decay broadens spectral peaks in observed spectra
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. … Or, as in the band-pass case described earlier, it would be due to an increase in the bandwidths occupied by the individual partials, or harmonics, of the sound. This would be the case if the envelope of the sound changed more rapidly. Figures 1.62 and 1.63 compare two similar systems—one with a slow and one with a fast rate of amplitude decay, the latter being due to a higher loss of energy from the system. The figures clearly show that in the system that decays more rapidly, there are more harmonics, and there is a higher bandwidth due to the more rapid change in the sound’s envelope. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 489 (
#corroborates, via linked claim)
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. … Figure 1.61 shows the effect of an increasing number of harmonics on a square wave. Or, as in the band-pass case described earlier, it would be due to an increase in the bandwidths occupied by the individual partials, or harmonics, of the sound. This would be the case if the envelope of the sound changed more rapidly. Figures 1.62 and 1.63 compare two similar systems—one with a slow and one with a fast rate of amplitude decay, the latter being due to a higher loss of energy from the system. The figures clearly show that in the system that decays more rapidly, there are more harmonics, and there is a higher bandwidth due to the more rapid change in the sound’s envelope. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 489 (
#expands, via linked claim)
Categorization
- XREF: connects to: Spectral broadening can mask source identity while preserving loudness-time function — Professor Dr.-Ing. Hugo Fastl, Professor Dr.-Ing. Eberhard, Psychoacoustics- Facts and Models, 1847; Long sound durations are required for narrow frequency spectra; Rapid changes in a sound’s amplitude envelope force broader spectral bandwidth — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 489 (+2 more)
Broader Connections
- Long sound durations are required for narrow frequency spectra
#corroborates(0.95) - Rapid changes in a sound’s amplitude envelope force broader spectral bandwidth
#corroborates(0.90) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 489 - Fast-changing acoustic signals necessarily occupy a wider spectral bandwidth.
#expands(0.90) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 489