(1-6) Reflection of auditorium seats and other surfaces

Reflection coefficients from a few other complicated surfaces

Thus, an apparent surface was given and reflection coefficient was defined for a complicated surface. Some other examples are given here picking up from past papers. I want to show how surface reflection is intuitively expressed and understood its physical behavior if it is done in the time domain.
It is expressed as an impulse response. It was inversely transformed from the transfer function with a high cut filter as it is done through my papers. Transfer functions are given as well.

A) Reflection coefficients of a few boundaries at Grosser Music Vereinssaal

Architectural plan in the above and section in the below of  Grosser Music Vereinssaal

Reflection coefficient of the pipe organ

The apparent surface of the pipe organ is given in the figure of the next paragraph. Time domain given in the figure means an impulse response of reflection.

Reflection coefficients for the pipe organ at the Musik Vereinssaal in Wien.

Presumption of reflection coefficients at an arbitrary incident angle

A reflection coefficient at an arbitrary incident angle is presumed as the product of the one at its horizontal angle and the one at its vertical angle. They were compared with measured results.
The following four figures show the reflection coefficient of the pipe organ at the normal incidence, at ( 0°,20°) in the horizontal, at ( 20°, 0°) in the vertical and at an oblique incidence ( 20°,20°) ,respectively. They are shown with dotted lines and compared with measured results which are given in thick lines.

Reflection coefficient of the audience space under the balcony which has women’s statues


There are women’s statues in the bottom of the audience space under the balcony. It gets the apparent or expedient surface as shown in the above figure. Reflection coefficients were measured in front of it and in the audience space.

The part which corresponds to the statue was taken from the measured reflection coefficient in front and it is compared with the one measured in the space.

Reflection coefficient of the expedient surface for the first balcony at both sides

Reflection coefficient of the tapestry which hangs at the wainscot under the balcony

There hangs a tapestry at the wainscot under the balcony and it is supposed an absorbent surface. Its reflection coefficient was measured. The local reactive assumption is applied at the incident angle of 40°and the calculated result is compared with the measurement in Figure 6.

Reflection coefficient of the standing place

The inside structure of the standing place in the bottom of the hall is complex. The reflection comes deep from the bottom. The reflection coefficient was measured when the expedient surface was set at the mouth of the standing place. It is shown in Figure 12. 

Reflection coefficient of the surface with Helmholz resonance absorbents

We got an opportunity to measure reflection coefficients of Helmholz resonance absorbent surface in the real wall of an auditorium. It was made of glass blocks having holes and being filled with fiber glass.

Wall section with Helmholz resonators

Wall surface with Helmholz resonators

The next three examples are possible to calculate to have their reflections and given their details in the homepage.

Reflection coefficients of the clouds at Tanglewood Music Shed

The triangle reflectors are hang on the stage at Tanglewood Music Shed, USA and called “Clouds”. They were made as a scale model for experiment.
Their reflection coefficients were calculated by the Rubinowicz line integral at the zero rear velocity potential. The rear rigid surface was given behind the clouds with an air space. Edge waves produced at the clouds were reflected secularly at the rigid rear surface on the calculation.

Reflection coefficient of a folded and leaning wall at Kyoto Kaikan Hall

The following folded and leaning lateral walls were used for the renovation on the stage at the above hall to have rich lateral reflections. See Fig. 9 and 10 of the page 68 in the reference of “Sound reflection of a curved rigid panel", J. Acoust. Soc. Jpn(E) 2, 2 (1981).

Reflection from a folded and leaned wall

mpulse response and transfer function of reflection of the folded and leaned wall

Impulse response and transfer function of reflection of the folded and leaned wall

Reflection from stage reflectors

When a reflector on the stage of the Kyoto Kaikan Hall was discussed, next tree types were calculated and measured. The details are given in Figs. 12 and 13 on pages 12 and 13 of the reference: “Sound reflection of a rigid plane panel and of the “live end” composed by those panels”, J. Acoust. Soc. Jpn(E)2, 1 (1981).

Plan                                         Section
Stage reflectors

Reflection of the ceiling (a)

Reflection of the ceiling (b)

Reflection of the ceiling (c)

There the early reflections are most important, and should be well discussed when they are used.