Chapter VI

My Acoustics

Yoshimasa Sakurai


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 for measurements.
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 system

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 wave.
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 point.
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 auditorium.

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 phenomenon.

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.

August 2012
At Kaiwaka, NZ
Yoshimasa Sakurai