Introduction to Acoustics

364 Part C Architectural Acoustics
Part C 10.2
the Grosser Musikvereinsaal is intermediate between
our results for the two factors. For the ceiling of the
hall, the height that maximized S1 was the lowest within
the allowed range of motion (Fig. 10.14a). This is due
to the fact that more energy can be provided from the
ceiling to the listening position throughout the seats.
To maximize S4, on the other hand, the ceiling took
on the maximum height in the possible range of motion
(Fig. 10.14b). Reflections from the flat ceiling did
not decrease the IACC, but those from the sidewalls
did.
Modification from the Shoe-Box
Next, to obtain even better sound fields, a little more
complicated form (model 2), as shown in Fig. 10.15,
was examined. The floor plan optimized according to
the above results was applied as a starting point. The
hall in its initial form was 14 m wide, the stage was
9 m deep, the room was 27 m long, and the ceiling was
15 m above the stage floor. The sound source was again
4.0 m from the front of the stage, but was 0.5 m to one
side of the centerline and 1.5 m above the stage floor.
The front and rear walls were vertically bisected to
obtain two faces, and each stretch of wall along the
side of the seating area was divided into four faces.
The walls were kept vertical (i. e., tilting was not al-
Stage
Sound source
Seats
Fig. 10.15 Initial scheme of the concert hall (model 2). The rear wall
of the stage and the rear wall of the audience area were divided into
two. Sidewalls were divided into four
lowed) to examine only the plan of the hall in terms
of maximizing S1 and S4. Each wall was moved independently
of the other walls. The openings between
the walls, in the acoustical simulation using the image
method, were assumed not to reflect the sound.
Forty-nine listening positions distributing throughout
the seating area on a 2 m×4 m grid were selected. In
the GA operation, the sidewalls were moved, so that
none of these 49 listening positions were excluded. The
moving range of each vertex was ±2 m in the direction
of the line normal to the surface. The coordinates of
the two bottom vertices of each surface were encoded
on the chromosomes for the GA. In this calculation,
the most preferred listening level was set for a point on
the hall’s long axis (central line), 10 m from the source
position.
Leaf-Shape Concert Hall
The result of optimizing the hall for S1 is shown in
Fig. 10.16 and the contour lines of equal S1 values are
shown in Fig. 10.17. To maximize S1, the rear wall of
the stage and the rear wall of the audience area took
on concave shapes. The result of optimizing for S4 is
shown in Fig. 10.18 and contour lines of equal S4 values
are shown in Fig. 10.19. To maximize S4, on the other
hand, the rear wall of the stage and the rear wall of the
audience area took on convex shapes. With regard to the
sidewalls, both S1 and S4 were maximized by the leafshaped
plan, which is discussed in the following section.
Fig. 10.16 A result for the model 2 optimized for S1