(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:
pulses of the same amplitude are heard as one pulse with interference.
-----------------Two positive pulses of the same amplitude start to be heard
in positive and negative signs of the same amplitude start
to be heard
3.5 〜 3.8ms -------Each of two pulses of the same
amplitude is heard same loud.
slightly larger than that of a
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
See the section of evoked potential.
Time window for an impact noise:
window for an impact noise
A singer at a choir does not like the delay from surrounding reflectors
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.
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
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
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
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 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
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