(2-3) Temporal aspect of an rectangular pulse of 0.05ms

Looking back the experiments in the past with 0.05ms rectangular pulses, its temporal aspect seems as in the following.

For two pulses:
-------------------------Two pulses of the same amplitude are heard as one pulse with interference.
1.4ms -----------------Two positive pulses of the same amplitude start to be heard split.
1.7ms------------------Two pulses in positive and negative signs of the same amplitude start
to be heard split.
3.5 〜 3.8ms -------Each of two pulses of the same amplitude is heard same loud.
slightly larger than that of a single pulse.
4 〜 5ms -----------Two pulses are heard completely separated, but its loudness is still
     50ms〜80ms---------Two successive pulses were heard three or more. Two non-correlated signals make Gestalt psychology. The inverse frequency of this range is 12〜20Hz.
                       α wave has 8〜13Hz, the lowest frequency of a pipe organ is 16Hz.
                       See the section of evoked potential.

Time window for an impact noise:
40ms-------------------Time window for an impact noise
                  A singer at a choir does not like the delay from surrounding reflectors (Harold Marshall)

The discrimination time of 1〜3ms by Hirsh is referred to papers by Walach, Newman and Rosenzueing and it was found at different directions. On the other hand, our results in the above were obtained at the median plane.
The loudness increase of two separate pulses may not only be caused by the pure tone of the time interval, but also by the integration in the time window owing to autocorrelation.
The rectangular pulse of 0.05ms is the fundamental quantity, but it is also an element to make non-correlation on our hearing system.

A sound field and the linear part of our hearing system have been solved referring to a rectangular pulse of 0.05ms. Accordingly, getting out somewhat confused frequency expression, the acoustical linear phenomena were properly arranged and grasped clearly.

A bit of additional experiments
Two rectangular pulses of 0.05ms were heard completely separated at the time interval of 5ms having a slight loudness increase, and the transient response was finished then. It was understood that the interference region of two rectangular pulses was over.
Now, if the number of the rectangular pulses is increased with the time interval how the loudness would be increased was experimented. The number was increase 2, 3, 4 and 5 and their loudness was compared with that of a single pulse.
The result is shown in Table 1. It shows how much loudness was increased judged by seven tested male students.

Table 1 Added loudness to the loudness of a rectangular pulse depending on the number of pulses

The arrangement of rectangular pulses and its spectral level is shown in Fig.1. It was arranged with only positive pulses in the left hand side and with positive and negative pulses in the right hand side.
For positive pulses only, the spectral level at 200Hz shows large. On the other hand for the positive and negative arrangement, the spectral level is dominant at 100Hz. They were caused by the equal time interval at arrangement, namely, a sort of the comb coloration.
Its envelope is increased as the number of pulses increases. When it is two, three, four, and five, it increases by 20log102=6dB, 20log103=9dB, 20log104=12dB and 20log105=14dB, respectively. The frequency characteristics of the transient response of hearing system are more sensitive in the low frequency range. A pulse arrangement gets its loudness by both of them.

       Positive pulses only                     Positive and negative pulses
Fig.1 Spectral level change with the number of pulses.

The next comparison was a pair comparison of positive pulses with positive and negative pulses when the number of pulses is the same as shown in the left of Table 2.
It was done twice. Every tested person was confused to answer at the first time but he was surer at the second time. It could be understood for them to be ready and have a path open.
Up to the four waves, they showed to feel B, positive and negative mixed, slightly louder
On the frequency characteristic until four waves, for the mutual arrangement of positive and negative they have large component at 100Hz and it is larger than the 200Hz component of only positive waves. The difference on loudness might be affected on the response, though 200Hz has most sensitive on the transient response of our hearing system.
However, the response to five waves was distributed and does not look to have clear difference. It must be interesting to discuss how a time window is given on this kind of waves. It might be given until 4 waves. It must be compared practically doing the integration for loudness.

Table 2 Pair comparison of positive pulses to positive and negative pulses at the same pulse number