Fast-changing acoustic signals necessarily occupy a wider spectral 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. … 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
Categorization
- XREF: The uncertainty principle analog — time-frequency tradeoff mirrors Heisenberg’s relation, a cross-domain parallel worth keeping. — connects to: Gaussian gating minimizes the bandwidth-duration product for tone bursts.; Faster sound decay broadens spectral peaks in observed spectra; Broadband sounds are easier to localize than narrowband sounds (+7 more)
- corroborated: 3 independent passages support this claim — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 489
Broader Connections
- Long sound durations are required for narrow frequency spectra
#corroborates(0.85) - Filtering a signal to narrow its bandwidth necessarily spreads it in time.
#expands(0.80)