What defines the length of a pulse (impulse-type sounds)? i.e. snaps, pops, crackles, bangs, bumps, and rattles.
The following 4 pulses are all white noise sustained for 37 ms, but each pulse has a different decay. Top left: No Decay. Top right: Linear decay of -12 db. Bottom left: Linear decay to -inf db. Bottom right: Inverse-log (exponential) decay to -inf db. Hear the pulses (warning: may be loud).
As you can tell, the last 2 pulses are clearly shorter in hearing. But strictly speaking, the last pulse does not hit -inf db until the end of 37 ms. Therefore, all pulses are technically 37 ms long.
Consequently, what is the true length of the pulses (in milliseconds) as heard by our ears?
Reason for question
I own a sound engineering handbook titled Handbook for Sound Engineers: The New Audio Cyclopedia (Second Edition), published 1987. The handbook has a pretty short subsection, under the section Psychoacoustics, titled Loudness of Impulses (subsection 2.10). Paired with this section is a diagram relating pulse width (length) with the change in loudness required to make the pulse sound as loud as whatever the pulse is played on top of.
Excerpts from that section:
This curve [Fig. 2-14] shows how much higher the level of short pulses of noise and pure tones must be to sound as loud as continuous noise or pure tones. Pluses longer than 200 ms are perceived to be as loud as continuous noise or tones of the same level. For the shorter pulses, the pulse level must be increased to maintain the same loudness as for the longer pulses.
A tad later in the secion:
Fig. 2-14 is one more indication that the ear has a time constant of about 200ms. This means that band levels should be measured with rms detectors having integration times of about 200 ms.
In the entire section (and inside the entire handbook for that fact), there is no part that describes how to define the pulse's width (length). Mysteriously, this section has no references. Therefore, I cannot correlate the section's information with a second source.