Noise envelope fluctuation rate is inversely proportional to bandwidth

Evidence

In the case of a band-pass noise with 200-Hz bandwidth, this means that envelope maxima should occur with an average distance of about 8 ms. … However, in this case, the bandwidth is only 20 Hz, the envelope fluctuates very slowly, and the temporal distance of envelope maxima increases on average to about 80 ms. The variation of the time function indicates that the narrow-band noise can be considered in a first approximation as a pure tone at 1 kHz, which is randomly amplitude modulated. — Professor Dr.-Ing. Hugo Fastl, Professor Dr.-Ing. Eberhard, Psychoacoustics- Facts and Models, 87

Categorization

• XREF: connects to: A sound’s time-domain rate of change determines its frequency-domain bandwidth — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 489