What is the true definition for the length of a pulse (impulse-type sounds)?

Question

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?

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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.

Answer 1

For an application such as this, I think that measurement of the pulse width can be somewhat arbitrary as long as you are measuring all pulses in the same way. For instance, pulses of 200ms or longer should be measured using the same methodology as shorter pulses.

This could be either to measure the start of the pulse being the first audio sample in the sequence that is non-zero and the end of the pulse being the last audio sample that is non-zero. This is one way of doing it, but perhaps a more realistic way would be to consider RMS levels of the pulses - that would better take into account decay.

Remember that the point of this exercise is to demonstrate a relative increase in level for pulses of shorter duration than 200ms to attain a similar perceived level of loudness to pulses that are 200ms or longer.

I don't think that the exact method is as important as the fact that everything is treated the same. Personally I would approach this by calculating an RMS level for each pulse and working out the start and end based on whether the RMS level exceeds a pre-determined level.

I do think that the author of the book should have addressed this point more clearly and the fact they have not done so is a valid point of criticism.