Acoustics of auditoriums

by Floyd Rowe Watson

B. DETAILS OF THE ACOUSTICAL SURVEY IN THE AUDITORIUM.

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.

Fig. 8. Longitudinal Section Showing how Sound Is Returned to the Stage to Form an Echo.

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.

Fig. 10. Plan of Auditorium Showing Action of Rear Wall on the Sound.

Fig. 11. Plan of Auditorium Showing Concentration of Sound by the Rear Wall.

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.

Fig. 13. Perspective of Stage Showing Focusing Action of Arch on Sound.

Fig. 14. Perspective of Stage Showing Focusing Action of Second Arch.

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.

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.

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.

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.