The general effect of the walls of the Auditorium on the sound may be
anticipated by considering analogous cases in geometrical optics, but
with the restrictions on “rays” described in the preceding paragraph.
The sound does not actually confine itself to the sharp boundaries
shown. The diagrams are intended to indicate the main effect of the
sound in the region so bounded. Fig. 7 gives such an idea for the
concentration of sound in the longitudinal section of the Auditorium.
The plan followed in the experimental work was to anticipate the path
of the sound as indicated in Fig. 7, then to verify the results with
the arc-light reflector. Figs. 8 and 9 show the effect of the rear
wall in the balcony in forming echoes on the stage. The speaker was
particularly unfortunate, being afflicted with no less than ten echoes.
[Illustration: FIG. 8. LONGITUDINAL SECTION SHOWING HOW SOUND IS
RETURNED TO THE STAGE TO FORM AN ECHO.]
[Illustration: FIG. 9. LONGITUDINAL SECTION SHOWING FORMATION OF ECHO
ON THE STAGE.]
The hard, smooth, circular wall bounding the main floor under the
balcony gave echoes as shown in Fig. 10, the sound going also in the
reverse direction of the arrows.
[Illustration: FIG. 10. PLAN OF AUDITORIUM SHOWING ACTION OF REAR WALL
ON THE SOUND.]
[Illustration: FIG. 11. PLAN OF AUDITORIUM SHOWING CONCENTRATION OF
SOUND BY THE REAR WALL.]
[Illustration: FIG. 12. THIS FIGURE TAKEN WITH FIG. 9 SHOWS HOW AN ECHO
IS SET UP ON THE STAGE.]
A more comprehensive idea of the action of this wall is shown in Fig.
11. This reflected sound was small in amount and therefore not a
serious disadvantage.
The cases cited were fairly easy to determine since the bundles of
sound considered were confined closely to either a vertical or a
horizontal plane for which the plans of the building gave some idea of
the probable path of the sound. For other planes, the paths followed
could be anticipated by analogy from the results already found. Fig. 12
shows in perspective the development of the result expressed in Fig. 9.
A square bundle of sound starts from the stage and strikes the
spherical surface of the dome. After reflection, it is brought to a
point focus, as shown, and spreads out until it strikes the vertical
cylindrical wall in the rear of the balcony. This wall reflects it to a
line focus, after which it proceeds to the stage. Auditors on all parts
of the stage complained of hearing echoes.
Referring to Fig. 7, it is seen that the arch over the stage reflects
sound back to the stage. Fig. 13 shows in perspective the focusing
action of this overhead arch. Fig. 14 shows the effect of the second
arch. Some of this sound is reflected to the stage and to the seats in
front of the stage; other portions, striking more nearly horizontally,
are reflected to the side balconies. The echoes are not strong except
for high pitched notes with short wave lengths, since the width of the
arch is small.
[Illustration: FIG. 13. PERSPECTIVE OF STAGE SHOWING FOCUSING ACTION OF
ARCH ON SOUND.]
[Illustration: FIG. 14. PERSPECTIVE OF STAGE SHOWING FOCUSING ACTION OF
SECOND ARCH.]
[Illustration: FIG. 15. TRANSVERSE SECTION SHOWING HOW MOST PRONOUNCED
ECHOES ARE SET UP BY THE TWO CONCAVE SURFACES.]
Passing now to the transverse section, Fig. 15, we find the most
pronounced echoes in the Auditorium. If an observer generates a sound
in the middle of the room directly under the center of the skylight,
distinct echoes are set up. A bundle of sound passes to the concave
surface which converges the sound to a focus, after which it spreads
out again to the other concave surface and is again converged to a
focus nearly at the starting point. The distance traveled is about
225 feet, taking about ¼ second, so that the conditions are right for
setting up a strong echo. This echo is duplicated by the sound which
goes in the reverse of the path just described. Another echo, somewhat
less strong, is formed by the sound that goes to the dome overhead
and which is reflected almost straight back, since the observer is
nearly at the center of the sphere of which the dome is a part. These
echoes repeat themselves, for the sound does not stop on reaching the
starting point but is reflected from the floor and repeats the action
just described. As many as ten distinct echoes have been generated by a
single impulse of sound.
[Illustration: FIG. 16. ACTION OF SOUND IN CAUSING ECHO ON THE STAGE.]
The echo shown in Fig. 15 is repeated in a somewhat modified form for
a sound generated on the stage by a speaker. Fig. 16 shows the path
taken by the sound. This echo is duplicated by the sound that goes in
the reverse direction of the arrows, so the speaker is greeted from
both sides. Fig. 17 is a perspective showing the path. The sound does
not confine itself closely to a geometrical pattern, as shown in the
picture, but spreads out by diffraction. The main effect is shown by
the figure.
[Illustration: FIG. 17. PERSPECTIVE SHOWING HOW AN ECHO IS FORMED ON
THE STAGE BY TWO REFLECTIONS. DIFFRACTION EFFECTS ARE NOT CONSIDERED IN
THIS DRAWING.]
Thus far only the echoes that reached the stage have been described.
Other echoes were found in other parts of the hall, and it seemed that
few places were free from them. The side walls in the balcony, for
instance, were instrumental in causing strong echoes in the rear of the
balcony. Fig. 18 shows in perspective the action of one of these walls.
These two surfaces were similar in shape and symmetrically placed. Each
was the upper portion of a concave surface with its center of curvature
in the center of the building under the dome. The general effect of
the left hand wall was to concentrate the sound falling on it in the
right hand seats in the balcony. Some of the sound struck the opposite
wall and was reflected to the stage, as shown in Fig. 17. Auditors who
sought the furthermost rear seats in the balcony to escape echoes were
thus caught by this unexpected action of the sound. The right hand wall
acted in a similar way to send the sound to the upper left balcony.
[Illustration: FIG. 18. PERSPECTIVE SHOWING SOUND REFLECTED FROM
CONCAVE WALL IN BALCONY. DIFFRACTION NOT CONSIDERED.]
The dome surface concentrates most of its sound near the front of the
central portion of the balcony and the ground floor in front of the
balcony in the form of a caustic cone. Figs. 7, 9 and 11 give some
conception of how a concentration of sound is caused by this spherical
surface. The echo in the front portion of the balcony was especially
distinct. On one occasion, in this place, the author was able to hear
the speaker more clearly from the echo than by listening to the direct
sound.
Minor echoes were set up by the horizontal arch surfaces in the
balcony. The sound from the stage was concentrated by reflection
from these surfaces and then passed to a second reflection from the
concave surfaces back of them. Auditors in the side balcony were thus
disagreeably startled by having sound come from overhead from the rear.