Acoustics has been my major professional work and a good friend of
mine. I could have enjoyed it with continuous progress. After I started
the sustainable project here at Kaiwaka, I got vacancy for a while, but
I have a lot of things to tell and leave for coming generations.
Here, I review my Acoustics that I have done, leave my messages for them and expect them to develop it.
The concept of frequency is originated from Music, I think. And it has
been used by transducer makers. We can not be strong enough to the
economical power here too. It has suppressed to hear beautiful sounds
of musical instruments or to hear wonderful music in a hall.
Namely, acoustical phenomena are given in time and space, but they were
recorded by a microphone and heard from loud speakers which were
characterized in the frequency domain. In other words, a sound field,
which must be expressed with a spatial impulse response, has been
treated not talking about it, but it was expressed with spectral
amplitudes to get temptation. This attitude led to big mistakes.
A bad example is competitive sales of loud speakers. Why has it been
said good to have flat frequency characteristics from low to high. If a
rectangular pulse is electrically given to such a loudspeaker, how the
output in the air is deformed into a complex form which is out of the
rectangular pulse. It is evident that the frequency characteristic is
not a measure for a loudspeaker’s quality. It must be difficult to
convolve its inverse filter to an input signal at processing, I guess.
When noise level is read on a noise level meter, it is given with
amplitude in dB. There is the fact that sound wave fluctuates around
the atmospheric pressure, but it has been referred unreasonably to
relate it for the response of our hearing system. Namely the real
background was hidden to be discussed.
Thinking about them in such a way, I write this chapter collecting my
past papers and giving some comments. I also plan to write a part of my
memorandum which was written when I visited world famous concert halls
This chapter is written in English and a brief introduction is given in Japanese in the beginning of each subject.
Without any words, a transfer function is the Fourier transform of an impulse response and the expression in the mapped space.
The expression in the frequency domain becomes perfect when the phase
angle is added to the amplitude. However, even if they are shown
together, it is impossible to imagine the real physical phenomenon
itself. When a transfer function is obtained to finish the discussion,
mentioning that the impulse response is found by its inverse Fourier
transform, any intuitive information is not given. Although an impulse
response includes the whole information, we have to understand how it
is related to the space. Otherwise, it can not be good information to
evaluate, for instance, an auditorium acoustics through our hearing
Firstly, I emphasize the importance of time response to be able to
imagine an acoustical phenomenon. For that, the acoustical phenomenon
is expressed as an impulse response.
When the rear velocity potentials of various plates are zero, namely,
the first reflection from their surfaces are calculated and compared
with measured results.
For a rigid surface of a plane panel, edge waves are produced after the
specular reflection. They are in negative and show its dimension. Once
they were called by a boundary wave but now I changed it to an edge
For a rigid curved surface, it is followed by edge waves and the specular reflection depends on its curvature.
For a surface with reflection coefficient, the contribution from the
specular reflection point is most important and it is defined at the
If it is defined such a way, its first reflection of a porous layer is
negative at the grazing angle. It happens at an auditorium seats to
decrease the direct sound loudness from the stage. An amphitheater
acoustics is explained referring to it.
For the mutual reflection of panels, it is shown that edge waves must be calculated properly.
For the early reflections in an auditorium, it is shown that the
reflections from the boundaries with the zero rear velocity potentials
predict them well. Edge waves of each boundary are specularly reflected
at the next boundary and also generate higher ordered edge waves. They
must explain the acoustical character of the enclosure. Thus calculated
early reflections were compared with measured results in a scale model
The diffraction over a semi-infinite wedge is shown to be produced by
the multiple reflection of the first diffraction at the wedge edge and
the half amplitude method is introduced.
The diffraction over a semi-infinite thick barrier is calculated with the method and compared with measured results.
The method was applied for the diffraction around a rectangular body and the result was well compared with measured results.
If the diffraction traveling along a semi-infinite wedge is expressed
by an impulse response it becomes zero at each end of a wedge of
limited length. This boundary condition around a body of limited
dimensions is very intuitive and practical to apply for an acoustical
The diffraction of a barrier with variety of shapes at the top is
discussed. The arrangement of the barriers is discussed as well.
The acoustics of a hand made amphitheater is explained why it is good.
Such a way, sound fields can be calculated inside and outside of an
enclosure in the form of an impulse response. When a sound field is
expressed in the time domain, our hearing system must be done to be
connected to it.
The transient response of human sensory system were obtained with
0.05ms rectangular pulse for its linier part. A weight can not be used
for the approximation of noise loudness of broad band, because it does
not include what is called non-linier responses, for instance, the
effect of the difference tones. The response to the 0.05ms rectangular
pulse is needed to evaluate a noise.
After the linier process there is a step to absolutize sound.
After then time window of integration of a sound was introduced to have its loudness.
The discrimination angle in the space is given with the change of head
related transfer function and the acoustic information in the angle
gets smoothing there.
When we evaluate the acoustics at a seat in an auditorium, first we get
the impulse response in the space. The hearing transient response which
is adjusted by the directivity of the head related transfer function is
convolved to the impulse response. The result is smoothed in the
discrimination angles. The visualized sound field with the help of
sight is used to see the sound field.
Environmental evaluation in a room must be done with not only noise
environment but other ones. Synthesized evaluation was given with two
other environments, thermal and light.
For a living environment, it has multiple factors to be evaluated
including noise environment. Multi valuable analysis was done and the
prediction method is given.
Transient responses were obtained for thermal sensation and brightness. It is important to discuss referring to each other.
Fusion of sight and audition is discussed. For the localization of a
sound source, learning from each one’s feature must be involved, so as
on the fusion of two sensory systems.
Evoked potential as a physiological aspect and acoustic emission were experimented with the 0.05ms rectangular pulse.
The overview of the above subjects could be expressed as follows:
Schematic overview of Acoustical fields in this report
I visited world famous concert halls for acoustical measurements from
April 1985 to March 1986 during my sabbatical year. I planned to find
the relationship between their reputations and acoustics, and find the
guideline for a good concert hall design.
An omni directional impact sound source was placed in the middle of a
stage and its direct sound and the sound at a receiving point in the
audience were simultaneously measured.
If there were absorptive surfaces, their reflection coefficients were
measured at the site. Detailed dimensions were measured and
architectural drawings were obtained as well. The impulse response at
any point in the audience could be calculated.
For the calculation of the early reflections of them, we started to get
their perspectives from the dimensions I measured and/or their
architectural drawings. How they were precisely reproduced was checked
through the stereoscopic views.
Now we got the Kobe earthquake. My lab was in a mess and those disks were spread around.
We had to stop working on them.
The concert halls I visited were as follows:
Bynjanei Haoma(Jerusalem, Israel)、Stadt Casino(Basel,
Switzerland)、Grosser Music Vereinssaal(Wien, Austria)、Concert Gebau
(Amsterdam, Holland)、Boston symphony Hall(Boston, USA)、Tanglewood Music
Shed(Massachusetts, USA) , Aula Magna(Caracas、Venezuela)、Teatro
Colon(Buenos Aires, Argentine), Christchurch Town Hall and Michael
Fowler Centre(New Zealand)
First, the calculated impulse response of a concert hall is compared
with the measured result to make sure the dimensions and surface finish
are properly given. The hearing transient response is convolved to it
and the result is smoothed in the discrimination space.
This expression is calculated from one seat to another and is observed
how it changes reflections there. This observation is compared with the
reputation in the hall.
We expect to have a few persons who are interested in the project and find out why those concert halls got good reputations.
As is mentioned above, the introduction of the rectangular pulse of
0.05ms that includes the audible frequency range make the discussions
on the calculations and measurements much clearer. We should make clear
and understand the linear system of sound fields and our hearing system.
Technology is only a little device to resist to the strong stream of economy.
We have to enhance it to direct to the right way. There we have to
analyze the response of a man and design it toward a better life.
I appreciate my sustainable project where I can look back in this way. Appreciations to Nature and the sun
Lastly I appreciate to my students graduated from my Lab, especially to
Hiroshi Morimoto with whom I will write a Japanese book with this title.
At Kaiwaka, NZ