Title: Acoustics of auditoriums : University of Illinois Bulletin, Vol. XI, March 16, 1914, No. 29
Author: Watson, Floyd Rowe
Language: English
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                    UNIVERSITY OF ILLINOIS BULLETIN

                             ISSUED WEEKLY

        Vol. XI              MARCH 16, 1914              No. 29

  Entered as second-class matter Dec. 11, 1912, at the Post Office at
             Urbana, Ill., under the Act of Aug. 24, 1912.


                        ACOUSTICS OF AUDITORIUMS

                                   BY
                              F. R. WATSON

                 [Illustration: UNIVERSITY OF ILLINOIS.
                            CHARTERED 1867.]

                            BULLETIN No. 73
                     ENGINEERING EXPERIMENT STATION

            PUBLISHED BY THE UNIVERSITY OF ILLINOIS, URBANA


                          PRICE: TWENTY CENTS

                             EUROPEAN AGENT
                     CHAPMAN AND HALL, LTD., LONDON



The Engineering Experiment Station was established by act of the
Board of Trustees, December 8, 1903. It is the purpose of the Station
to carry on investigations along various lines of engineering and
to study problems of importance to professional engineers and to
the manufacturing, railway, mining, constructional, and industrial
interests of the State.

The control of the Engineering Experiment Station is vested in the
heads of the several departments of the College of Engineering. These
constitute the Station Staff and, with the Director, determine the
character of the investigations to be undertaken. The work is carried
on under the supervision of the Staff, sometimes by research fellows as
graduate work, sometimes by members of the instructional staff of the
College of Engineering, but more frequently by investigators belonging
to the Station corps.

The results of these investigations are published in the form of
bulletins, which record mostly the experiments of the Station’s own
staff of investigators. There will also be issued from time to time
in the form of circulars, compilations giving the results of the
experiments of engineers, industrial works, technical institutions, and
governmental testing departments.

The volume and number at the top of the title page of the cover are
merely arbitrary numbers and refer to the general publications of the
University of Illinois; _either above the title or below the seal
is given the number of Engineering Experiment Station bulletin or
circular, which should be used in referring to these publications_.

For copies of bulletins, circulars, or other information address the
Engineering Experiment Station, Urbana, Illinois.

[Illustration: FIG. 1. AUDITORIUM, UNIVERSITY OF ILLINOIS.]



ACOUSTICS OF AUDITORIUMS

AN INVESTIGATION OF THE ACOUSTICAL PROPERTIES OF THE AUDITORIUM AT THE
UNIVERSITY OF ILLINOIS.



I. INTRODUCTION.


Much concern has arisen in late years in the minds of architects
because of the faulty acoustics that exist in many auditoriums. The
prevalence of echoes and reverberations with the consequent difficulty
in hearing and understanding on the part of the auditor defeats the
purpose of the auditorium and diminishes its value.

The Auditorium at the University of Illinois presents such a case. The
building is shaped nearly like a hemisphere, with several large arches
and recesses to break up the regularity of its inner surface. The
original plans of the architect were curtailed because of insufficient
money appropriated for the construction. The interior of the hall,
therefore, was built absolutely plain with almost no breaking up of the
large, smooth wall surfaces; and, at first, there were no furnishings
except the seats and the cocoa matting in the aisles. The acoustical
properties proved to be very unsatisfactory. A reverberation or undue
prolongation of the sound existed, and in addition, because of the
large size of the room and the form and position of the walls, echoes
were set up.

If an observer stood on the platform and clapped his hands, a veritable
chaos of sound resulted. Echoes were heard from every direction and
reverberations continued for a number of seconds before all was still
again. Speakers found their utterances thrown back at them, and
auditors all over the house experienced difficulty in understanding
what was said. On one occasion the University band played a piece which
featured a xylophone solo with accompaniment by the other instruments.
It so happened that the leader heard the echo more strongly than the
direct sound and beat time with it. Players near the xylophone kept
time to the direct sound, while those farther away followed the echo.
The confusion may well be imagined.

Thus it seemed that the Auditorium was doomed to be an acoustical
horror; that speakers and singers would avoid it, and that auditors
would attend entertainments in it only under protest. But the apparent
misfortune was in one way a benefit since it provided an opportunity
to study defective acoustics under exceptionally good conditions
and led to conclusions that not only allowed the Auditorium to be
improved but also indicate some of the pitfalls to be avoided in future
construction of other halls.

[Illustration: FIG. 2. PHOTOGRAPH OF INTERIOR. VIEW OF STAGE.]

[Illustration: FIG. 3. PHOTOGRAPH OF INTERIOR. VIEW TOWARD BALCONY.]

An investigation of the acoustical properties of the Auditorium was
begun in 1908 and has continued for six years. It was decided at the
outset not to use “cut and try” methods of cure, but to attack the
problem systematically so that general principles could be found, if
possible, that would apply not only to the case being investigated but
to auditoriums in general. This plan of procedure delayed the solution
of the problem, since it became necessary to study the theory of sound
and carry out laboratory investigations at the same time that the
complex conditions in the Auditorium were being considered. The author
spent one year of the six abroad studying the theory of acoustics and
inspecting various auditoriums.

The main echoes in the Auditorium were located by means of a new method
for tracing the path of sound, the time of reverberation was determined
by Sabine’s method, and a general diagnosis of the acoustical defects
was made. Hangings and curtains were installed in accordance with the
results of the study so that finally the acoustical properties were
improved.

_Acknowledgment._--The author desires to express his great appreciation
of the advice and encouragement given by President E. J. James,
Supervising Architect J. M. White, and Professor A. P. Carman of
the Physics Department. He desires also to acknowledge the material
assistance cheerfully rendered by the workmen at the University, which
contributed in no small degree to the successful solution of the
problem.



II. BEHAVIOR OF SOUND WAVES IN A ROOM.


When a speaker addresses an audience, the sounds he utters proceed in
ever widening spherical waves until they strike the boundaries of the
room. Here the sound is partly reflected, partly transmitted, and the
rest absorbed. The amounts of reflection, absorption and transmission
depend on the character of the walls. A hard, smooth wall reflects most
of the sound so that but little is transmitted or absorbed. In the case
of a porous wall or a yielding wall, the absorption and transmission
are greater, and the reflection is less. After striking a number of
reflecting surfaces, the energy is used up and the sound dies out.

The reflection of sound produces certain advantages and disadvantages
for the acoustics. When it is considered that sound travels about 1100
feet a second it may be seen that a room of ordinary size is almost
immediately filled with sound because of the many reflections. In a
room 40 feet square, for instance, the number of reflections per second
between opposite walls is 1100 ÷ 40, or approximately 27. The number is
really greater than this, since the sound that goes into the corners
is reflected much more frequently than out in the middle where the
distances between walls are greater. The result is that the sound mixes
thoroughly in all parts of the room so as to give the same average
intensity; that is, the sound is of the same average _loudness_ for all
auditors, even for those in the remotest corners.

Though the reflection of sound has the advantage of fulfilling the
conditions for loudness, it introduces at the same time possibilities
for setting up defective acoustics. For instance, when the walls of the
room are hard and smooth very little energy is lost at each impact of
the sound and many reflections take place before it finally dies out.
This slow decadence of the sound, or _reverberation_ as it is called,
is the most common defect in auditoriums.

If a speaker talks in such a hall the auditors have difficulty in
understanding. Each sound, instead of dying out quickly, persists for
some time so that the succeeding words blend with their predecessors
and set up a mixture of sounds which produces confusion. The cure for
the trouble is brought about by the introduction of materials such as
carpets, tapestries, and the like, which act as absorbers of sound and
reduce the time of reverberation.

When music is played in an auditorium with a prolonged reverberation,
the tones following one another blend and produce the same effect as
that of a piano when played with the loud pedal in use. A reverberation
is more advantageous for music than for speech, since the prolongation
and blending of the musical tones is desired, but the mixing of the
words in a speech is a distinct disadvantage. When curing this defect
for halls used for both music and speaking, a middle course must be
steered, so that the reverberation is made somewhat long for speaking
and somewhat short for music, yet fairly satisfactory for both.

Going back to the consideration of the reflection of sound, it is found
that another defect may be produced, namely, an _echo_. This is the
case when a wall at some distance reflects the sound to the position
of the auditor. He hears the sound first from the speaker, then later
by reflection from the wall. The time interval between the direct and
reflected sound must be great enough to allow two distinct impressions
to be made. This time is about 1/15 of a second, but varies with the
acuteness of the observer. The farther off the wall is, the greater is
the time interval and the more pronounced is the echo. If the wall is
not very distant, the time interval is too short to allow two distinct
impressions to be made, and the effect on the auditor is then much the
same as if his neighbor at his side speaks the words of the discourse
in his ear at the same time that he gets them directly from the
speaker. In case the reflecting wall is curved so as to focus the sound
the echoes are much more pronounced. A curved wall wherever it may be
placed in an auditorium is thus always a menace to good acoustics.

There are other actions of the sound that may result in acoustical
defects. The phenomena of _resonance_, for instance, may cause trouble.
Suppose that the waves of sound impinge on an elastic wall, not too
rigid. If these waves are timed right they set the wall in vibration in
the same way that the bell ringer causes a bell to ring by a succession
of properly timed pulls on the bell rope. The wall of the room will
then vibrate under the action of this sound with which it is in tune
and will reinforce it. Now suppose a band is playing in a room. Certain
tones are reinforced, while the others are not affected. The original
sound is then distorted. The action is the same on the voice of the
speaker. The sounds he utters are complex and as they reach the walls
certain components are reinforced and the quality of the sound is
changed. This action of resonance may also be caused by the air in a
room. Each room has a definite pitch to which it responds, the smaller
the volume of the room the higher being the pitch. A large auditorium
would respond to the very low pitch of the bass drum. In small rooms
and alcoves the response is made to higher pitched tones, as may be
observed by singing the different notes of the scale until a resonance
is obtained.

Another action of sound causes the _interference_ of waves. Thus the
reflected waves may meet the oncoming ones and set up concentrations of
sound in certain positions and a dearth of sound in others.

Summing up, it is seen that the effects of sound which may exist in
a room are _loudness_, _reverberation_, _echoes_, _resonance_, and
_interference_, and that the most common defects are reverberation and
echoes. We now turn to the discussion of the methods of cure.



III. METHODS OF IMPROVING FAULTY ACOUSTICS.


A. REVERBERATION AND ITS CURE.

Everyone has doubtless observed that the hollow reverberations in
an empty house disappear when the house is furnished. So, in an
auditorium, the reverberation is lessened when curtains, tapestries,
and the like are installed in sufficient numbers. The reason for this
action is found when we inquire what ultimately becomes of the sound.

Sound is a form of energy and energy can not be destroyed. When it
finally dies out, the sound must be changed to some other form of
energy. In the case of the walls of a room, for instance, it has been
shown in a preceding paragraph that the sound may be changed into
mechanical energy in setting these walls in vibration. Again, some
of the sound may pass out through open windows and thus disappear.
The rest of the sound, according to Lord Rayleigh, is transformed by
friction into heat. Thus[1] a high pitched sound, such as a hiss,
before it travels any great distance is killed out by the friction of
the air. Lower pitched sounds, on reaching a wall, set up a friction
in the process of reflection between the air particles and the wall so
that some of the energy is converted into heat.[2] The amount of sound
energy thus lost is small if the walls are hard and smooth. The case is
much different, however, if the walls are rough and porous, since it
appears that the friction in the pores dissipates the sound energy into
heat. In this connection, Lamb[3] writes: “In a sufficiently narrow
tube the waves are rapidly stifled, the mechanical energy lost being
of course converted into heat. * * * * When a sound wave impinges on a
slab which is permeated by a large number of very minute channels, part
of the energy is lost, so far as the sound is concerned, by dissipation
within these channels in the way just explained. The interstices in
hangings and carpets act in a similar manner, and it is to this cause
that the effect of such appliances in deadening echoes in a room is
to be ascribed, a certain proportion of the energy being lost at each
reflection. It is to be observed that it is only through the action of
true dissipative forces, such as viscosity and thermal conduction, that
sound can die out in an enclosed space, no mere modifications of the
waves by irregularities being of any avail.”

It should be pointed out in this connection that any mechanical
breaking up of the sound by relief work on the walls or by obstacles in
the room will not primarily diminish the energy of the sound. These
may break up the regular reflection and eliminate echoes, but the sound
energy as such disappears only when friction is set up.

The following quotation from Rayleigh[4] emphasizes these conclusions:
“In large spaces, bounded by non-porous walls, roof, and floor,
and with few windows, a prolonged resonance seems inevitable. The
mitigating influence of thick carpets in such cases is well known. The
application of similar material to the walls and roof appears to offer
the best chance of further improvement.”

_Experimental Work on Cure of Reverberation._--The most important
experimental work in applying this principle of the absorbing power of
carpets, curtains, etc., has been done by Professor Wallace C. Sabine
of Harvard University.[5] In a set of interesting experiments lasting
over a period of four years, he was able to deduce a general relation
between _t_, the time of reverberation, _V_, the volume of the room,
and _a_, the absorbing power of the different materials present. Thus:

                       _t_ = 0.164 _V_ ÷ _a_ (1)

For good acoustical conditions, that is, for a short time of
reverberation, the volume _V_ should be small and the absorbing
materials, represented by _a_, large. This is the case in a small room
with plenty of curtains and rugs and furniture. If, however, the volume
of the room is great, as in the case of an auditorium, and the amount
of absorbing materials small, a troublesome reverberation will result.

Professor Sabine determined the absorbing powers of a number of
different materials. Calling an open window a perfect absorber of
sound, the results obtained may be written approximately as follows:

    One square meter of open window space             1.000
    One square meter of glass, plaster, or brick       .025
    One square meter of heavy rugs, curtains, etc.     .25
    One square meter of hair felt, 1 inch thick        .75
    One square meter of audience                       .96

These values, together with the formula, allow a calculation to be made
in advance of construction for the time of reverberation. This pioneer
work cleared the subject of architectural acoustics from the fog of
mystery that hung over it and allowed the essential principles to be
seen in the light of scientific experiment.

In a later investigation[6] Sabine showed that the reverberation
depended also on the pitch of sound. As a concrete example, the high
notes of a violin might be less reverberant with a large audience
than the lower tones of the bass viol, although both might have the
same reverberation in the room with no audience. Again, the voice of
a man with notes of low pitch might give satisfactory results in an
auditorium while the voice of a woman with higher pitched notes would
be unsatisfactory.

These considerations show that the acoustics in an auditorium vary with
other factors than the volume of the room and the amount of absorbing
material present. The audience may be large or small, the speaker’s
voice high or low, the entertainment a musical number or an address.
The best arrangement for good acoustics is then a compromise where the
average conditions are satisfied. The solution offered by Professor
Sabine is such an average one, and has proved satisfactory in practice.

The problem of architectural acoustics has been attacked experimentally
by other workers. Stewart[7] proposed a cure for the poor acoustical
conditions in the Sibley Auditorium at Cornell University. His
experiments confirmed the work of Sabine. Marage[8], after
investigating the properties of six halls in Paris, approved Sabine’s
results and advocated a time of reverberation of from ½ to 1 second for
the case of speech.

_Formulae for Reverberation of Sound in a Room._--On the theoretical
side, Sabine’s formula has been developed by Franklin,[9] who obtained
the relation _t_ = 0.1625 _V_ ÷ _a_, an interesting confirmation, since
Sabine’s experimental value for the constant was 0.164.

A later development has been given by Jäger,[10] who assumes for a room
whose dimensions are not greater than about 60 feet, that the sound,
after filling the room, passes equally in all directions through any
point, and that the average energy is the same in different parts of
the room. By using the theory of probability and considering that a
beam of sound in any direction may be likened to a particle with a
definite velocity, he was able to deduce Sabine’s formula and write
down the factors that enter into the constants. Applying his results to
the case of reflection of sound from a wall, he showed that sound would
be reflected in greater volume when the mass of the wall was increased
and the pitch of the sound made higher. He showed also that when sound
impinges on a porous wall, more energy is absorbed when the pitch of
the sound is high than when it is low, since the vibrations of the air
are more frequent, and more friction is introduced in the interstices
of the material.


B. ECHOES AND THEIR REMEDY.

An echo is set up by a reflecting wall. If an observer stands some
distance from the front of a cliff and claps his hands, or shouts, he
finds that the sound is returned to him from the cliff as an echo. So,
in an auditorium, an auditor near the speaker gets the sound first
directly from the speaker, then, an instant later, a strong repetition
of the sound by reflection from a distant wall. This echo is more
pronounced if the wall is curved and the auditor is at the point where
the sound is focused.

To cure such an echo, two methods may be considered. One method
consists in changing the form of the wall so that the reflected sound
no longer sets up the echo. That is, either change the angle of the
wall, so that the reflected sound is sent in a new direction where it
may be absorbed or where it may reinforce the direct sound without
producing any echoes, or else modify the surface of the wall by relief
work or by panels of absorbing material, so that the strong reflected
wave is broken up and the sound is scattered. The second method is to
make the reflecting wall a “perfect” absorber, so that the incident
sound is swallowed up and little or none reflected. These methods
have been designated as “surgical” and “medicinal” respectively. Each
method has its disadvantages. Changing the form of the walls in an
auditorium is likely to do violence to the architectural design. On
the other hand, there are no perfect absorbers, except open windows,
and these can seldom be applied. The cure in each case is, then, a
matter of study of the special conditions of the auditorium. Usually
a combination of the surgical and the medicinal cures is adopted. For
instance, coffering a wall so that panels of absorbing material may be
introduced has been found to work well in bettering the acoustics, and
also, in many cases, it fits in with the architectural features.


C. POPULAR CONCEPTION OF CURES.--USE OF WIRES AND SOUNDING BOARDS.

A few words should be written concerning the popular notion that
wires and sounding boards are effective in curing faulty acoustics.
Experiments and observations show that wires are of practically no
benefit, and sounding boards can be used only in special cases. Wires
stretched in a room scarcely affect the sound, since they present too
small a surface to disturb the waves. They have much the same effect on
sound waves that a fish line in the water has on water waves. The idea
has, perhaps, grown into prominence because of the action of a piano
in responding to the notes of a singer. The piano has every advantage
over a wire in an auditorium. It has a large number of strings tuned
to different pitches so that it responds to any note sung. It also has
a sounding board that reinforces strongly the sound of the strings.
Finally, the singer is usually near the piano. The wire in the
auditorium responds to only one tone of the many likely to be present,
it has no sounding board, and the singer is some distance away. But
little effect, therefore, is to be expected.

The author has visited a number of halls where wires have been
installed, and has yet to find a case where pronounced improvement has
resulted.[11] Sabine[12] cites a case where five miles of wire were
stretched in a hall without helping the acoustical conditions. It is
curious that so erroneous a conception has grown up in the public mind
with so little experimental basis to support it.

_Sounding Boards._--Sounding boards or, more properly, reflecting
boards, have value in special cases. Some experiments are described
later where pronounced effects were obtained. The sounding board should
be of special design to fit the conditions under which it is to be used.

_Modeling New Auditoriums after Old Ones with Good Acoustics._--Another
suggestion often made is for architects to model auditoriums after
those already built that have good acoustical properties. It does not
follow that halls so modeled will be successful, since the materials
used in construction are not the same year after year. For instance,
a few years ago it was the usual custom to put lime plaster on wooden
lath; now it is frequently the practice to put gypsum plaster on metal
lath, which forms an entirely different kind of a surface. This latter
arrangement makes hard, non-porous walls which absorb but little sound,
and thus aggravate the reverberation. Further, a new hall usually is
changed somewhat in form from the old one, to suit the ideas of the
architect, and it is very likely that the changes will affect the
acoustics.


D. THE EFFECT OF THE VENTILATION SYSTEM ON THE ACOUSTICS.

At first thought it might seem that the ventilation system in a room
would affect the acoustical properties. The air is the medium that
transmits the sound. It has been shown that the wind has an action
in changing the direction of propagation of sound.[13] Sound is also
reflected and refracted at the boundary of gases that differ in density
and temperature.[14] It is found, however, that the effect of the
usual ventilation currents on the acoustics in an auditorium is small.
The temperature difference between the heated current and the air in
the room is not great enough to affect the sound appreciably, and the
motion of the current is too slow and over too short a distance to
change the action of the sound to any marked extent.[15]

Under special circumstances, the heating and ventilating systems may
prove disadvantageous.[16] A hot stove or a current of hot air in the
center of the room will seriously disturb the action of sound. Any
irregularity in the air currents so that sheets of cold and heated air
fluctuate about the room will also modify the regular action of the
sound and produce confusion. The object to be striven for is to keep
the air in the room as homogeneous and steady as possible. Hot stoves,
radiators, and currents of heated air should be kept near the walls and
out of the center of the room. It is of some small advantage to have
the ventilation current go in the same direction that the sound is to
go, since a wind tends to carry the sound with it.



IV. THE INVESTIGATION IN THE AUDITORIUM AT THE UNIVERSITY OF ILLINOIS.


A. PRELIMINARY WORK.

As already stated, a chaos of sound was set up when an observer in
the Auditorium spoke or shouted or clapped his hands. Both echoes and
reverberations were present and could be heard in all parts of the
room, though the echoes seemed to be strongest on the stage and in
the balcony. The prospects for bettering the acoustics were not very
encouraging. Luckily, the cure for the reverberation was fairly simple,
since Sabine’s method gave a definite procedure that could be applied
to this case. The cure for the echo, however, was yet to be found. It
was first necessary to find out which walls set up the defect.

The attempt to locate echoes by generating a sound and listening with
the ear met with only partial success. The ear is sensitive enough but
becomes confused when many echoes are present, coming apparently from
every direction, so that the evidence thus obtained is not altogether
conclusive. It became apparent that the successful solution lay in
fixing the attention on the sound going in a particular direction and
finding out where it went after reflection; then tracing out the path
in another particular direction, and so on until the evidence obtained
gave some hint of the general action of the sound.

[Illustration: FIG. 4. WATCH AS SOURCE OF SOUND, BACKED BY A CONCAVE
REFLECTOR.]

The first step in the application of this principle was to use a
faint sound which could not be heard at any great distance unless
reinforced in some way. The ticks of a watch were directed, by means
of a reflector (Fig. 4) to certain walls suspected of giving echoes.
Using the relation that the angle of incidence equals the angle of
reflection, the reflected sound was readily located, and the watch
ticks heard distinctly after they had traveled a total distance as
great as 70 to 80 feet from the source.

In a later experiment, a metronome was used which gave a louder
sound. It was enclosed in a sound-proof structure (Fig. 5) with only
one opening, so that the sound could be directed by means of a horn.
This method was suggested by the work of Gustav Lyon in the Hall of
the Trocadero at Paris,[17] where a somewhat similar arrangement was
used. The method was successful and verified the observations taken
previously.

[Illustration: FIG. 5. METRONOME AS SOURCE OF SOUND.]

[Illustration: FIG. 6. ARC-LIGHT AS SOURCE OF SOUND.]

Though the results obtained with the watch and metronome seemed
conclusive, yet the observer was not always confident of the results. A
further method was sought, and a more satisfactory one found by using
an alternating current arc-light at the focus of a parabolic reflector
(Fig. 6). In addition to the light, the arc gave forth a hissing sound,
which was of short wave length and therefore experienced but little
diffraction. The bundle of light rays was, therefore, accompanied by
a bundle of sound, both coming from the same source and subject to
the same law of reflection. The path of the sound was easily found by
noting the position of the spot of light on the wall. The reflected
sound was located by applying the relation that the angles of incidence
and reflection are equal. The arc-light sound was intense and gave the
observer confidence in results that was lacking in the other methods.
To trace successive reflections, small mirrors were fastened to the
reflecting walls so that the path of the reflected sound was indicated
by the reflected light. A “diagnosis” of the acoustical troubles of the
Auditorium was then made by this method.

It should be noted here that the arc-light sound is not the same as the
sounds of music or speech, these latter ones being of lower pitch and
of longer wave length. It was, therefore, a matter of doubt whether the
results obtained would hold also for the case of speech or music. Tests
made by observers stationed in the Auditorium when musical numbers
and speeches were rendered, however, verified the general conclusions
obtained with the arc-light.

It should be pointed out in this connection that there is an objection
to applying the “ray” method of geometrical optics to the case of
sound. It is much more difficult to get a ray of sound than it is to
get a ray of light.[18] This is due to the difference in the wave
lengths in the two cases. It appears that the waves are diffracted,
or spread out, in proportion to their length, the longer waves being
spread out to a greater extent. The short waves of light from the sun,
for instance, as they come through a window mark out a sharp pattern
on the floor, which shows that the waves proceed in straight lines
with but little diffraction or spreading. Far different is it with
the longer waves of sound. If the window is open, we are able to hear
practically all the sounds from outdoors, even that of a wagon around
the corner, although we may be at the other end of the room away from
the window. The longer sound waves spread out and bend at right angles
around corners, so that it is almost impossible to get a sound shadow
with them. Furthermore, in the matter of reflection, it appears that
the area of the reflecting wall must be comparable with the length of
the waves being reflected. In the case of light, the waves are very
minute, hence a mirror can be very small and yet be able to set up a
reflection; but sound waves are of greater length, the average wave
length of speech (45 cm.) being about 700 000 times longer than the
wave length of yellow light (.00006 cm.), hence the reflecting surface
must be correspondingly larger. An illustration will perhaps make
this clearer. Suppose a post one foot square projects through a water
surface. The small ripples on the water will be reflected easily from
the post, but the large water waves pass by almost as if the post were
not there. The reflecting surface must have an area comparable with
the size of the wave if it is to cause an effective reflection. Relief
work in auditoriums, if of small dimensions, will affect only the high
pitched sounds, i. e., those of short wave length, while the low
pitched sounds of long wave length are reflected much the same as from
a rather rough wall. It is also shown that the area of the reflecting
surface is dependent on its distance from the source of sound and from
the observer; the greater these distances are the larger must be the
reflecting surface.[19]

These considerations all show that the reflection of sound is a
complicated matter. The dimensions of a wall to reflect sound, or of
relief work to scatter it, are determined by the wave length and by
the various other factors mentioned. It should be said with caution
that a “ray” of sound is reflected in a definite way from a small bit
of relief work. We must deal with _bundles_ of sound, not too sharply
bounded, and have them strike surfaces of considerable area in order to
produce reflections with any completeness.

[Illustration: FIG. 7. LONGITUDINAL SECTION SHOWING THE CHIEF
CONCENTRATIONS OF SOUND, THE DIFFRACTION EFFECTS BEING DISREGARDED.]


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.

[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.


C. CONCLUSION DRAWN FROM THE ACOUSTICAL SURVEY.

The results of the survey show that curved walls are largely
responsible for the formation of echoes because they concentrate the
reflected sound. It seems desirable, therefore, to emphasize the danger
of using such walls unless their action is annulled by absorbing
materials or relief work. Large halls with curved walls are almost sure
to have acoustical defects.


D. METHODS EMPLOYED TO IMPROVE THE ACOUSTICS.

_Reflecting Boards._--The provisional cure was brought about gradually
by trying different devices suggested by the diagnosis. In one set
of experiments sounding boards of various shapes and sizes were
used. A flat board about five feet square placed at an incline over
the position of the speaker produced little effect. A larger canvas
surface, about 12 by 20 feet, was not much better. A parabolic
reflector, however, gave a pronounced effect. This reflector was
mounted over a pulpit at one end of the stage and served to intercept
much of the sound that otherwise would have gone to the dome and
produced echoes. The path of the reflected sound was parallel to the
axis of the paraboloid of which the reflector was a quarter section.
There was no difficulty in tracing out the reflected sound. Auditors in
the path of the reflected rays reported an echo, but auditors in other
parts of the Auditorium were remarkably free from the usual troubles.
The device was not used permanently, since many speakers objected to
the raised platform. Moreover, it was not a complete cure, since it was
not suited for band concerts and other events, where the entire stage
was used. Another reflector similar in shape to the one just described
is shown in Figs. 21 and 22.

[Illustration: FIG. 19. REFLECTING BOARD IN PROCESS OF CONSTRUCTION.]

[Illustration: FIG. 20. FINISHED REFLECTOR. HARD PLASTER ON WIRE LATH.]

_Sabine’s Method._--The time of reverberation was determined by
Sabine’s method. An organ pipe making approximately 526 vibrations a
second was blown for about three seconds and then stopped. An auditor
listened to the decreasing sound, and when it died out made a record
electrically on a chronograph drum. The time of reverberation was found
to be 5.90 seconds, this being the mean of 19 sets of measurements,
each of about 20 observations. The reverberation was found also by
calculation from Sabine’s equation (see Section III), taking the
volume of the Auditorium as 11,800 cubic meters and calculating the
absorbing power of all the surfaces in the room. This calculation gave
6.4 seconds. The agreement between the two results is as close as could
be expected, since neither the intensity of the sound nor the pitch
used by the author was the same as those used by Professor Sabine, and
both of these factors affect the time of reverberation.

[Illustration: FIG. 21. PARABOLIC REFLECTOR SHOWING ITS ACTION ON
SOUND.]

[Illustration: FIG. 22. PHOTOGRAPH OF PARABOLIC REFLECTOR.]

Several years later the time of reverberation was again determined
after certain changes had been made. A thick carpet had been placed
on the stage, heavy velour curtains 18 by 32 feet in area hung on the
wall at the rear of the stage, a large canvas painting 400 square feet
in area was installed, and the glass removed from the skylight in the
ceiling. The time of reverberation was reduced to 4.8 seconds. With an
audience present this value was reduced still more, and when the hall
was crowded at commencement time the reverberation was not troublesome.

_Method of Eliminating Echoes._--Although the time of reverberation
was reduced to be fairly satisfactory, as just explained, the echoes
still persisted, and were very annoying. Attempts were made to reduce
individual echoes by hanging cotton flannel on the walls at critical
points. Thus the shaded areas in Fig. 17 were covered and also the
entire rear wall in the balcony. Pronounced echoes still remained, and
it was evident that some drastic action was necessary to alleviate this
condition. Four large canvases, shown in Figs. 23 and 24, were then
hung in the dome in position suggested by the results of the diagnosis.
A very decided improvement followed. For the first time the echoes were
reduced to a marked degree and speakers on the stage could talk without
the usual annoyance. This arrangement eliminated the echoes not only on
the stage, but generally all over the house. A number of minor echoes
were still left, but the conditions were much improved, especially when
a large audience was present to reduce the reverberation.

_Proposed Final Cure._--The state of affairs just described is the
condition at the time of writing. Two propositions were considered in
planning the final cure. One proposition involved a complete remodeling
of the interior of the Auditorium. Plans of an interior were drawn
in accordance with the results of the experimental work that would
probably give satisfactory acoustics. This proposition was not carried
out because of the expense and because it was thought desirable to
attempt a cure without changing the shape of the room. The latter
plan is the one now being followed. It is proposed to replace the
present unsightly curtains with materials which will conform to the
architectural features of the Auditorium and which will have a pleasing
color scheme. At the same time, it will be necessary to hold to the
features which have improved the acoustics.

[Illustration: FIG. 23. PHOTOGRAPH OF TWO OF THE CANVAS CURTAINS IN THE
DOME OF THE AUDITORIUM. NOTE ALSO THE ABSORBING MATERIALS UNDER THE
ARCHES.]

[Illustration: FIG. 24. PHOTOGRAPH OF DOME OF AUDITORIUM SHOWING THE
CANVASES INSTALLED TO ELIMINATE ECHOES.]



V. BIBLIOGRAPHY OF PUBLICATIONS ON ACOUSTICS OF AUDITORIUMS.


_Auerbach, F._ “Akustik.” Winkelmann’s Handbuch der Physik, Vol. II,
1909. An encyclopædia of acoustics, the following topics applying
to the subject in hand: “Akustik der Gebäude,” pp. 580–584, with
references. “Nachhall und Echo,” pp. 565–569, with references.

_Blackall, C. H._ “Acoustics of Audience Halls,” Engineering Record,
Vol. 45, pp. 541–542, 1902. A paper recording the opinions of the
author with many references to acoustical properties of particular
audience halls.

_Cornelison, R. W._ “The Acoustical Properties of Rooms Particularly as
Affected by Wall Coverings,” 1905. A pamphlet describing the merits of
“Fabrikona” burlap as a sound absorber. H. B. Wiggin’s Sons Company,
Bloomfield, N. J.

_Eichhorn, A._ “Die Akustik Grosser Raüme nach Altgriechischer
Theorie.” Ernst and Korn, Publishers, Berlin, 1888. A discussion of
Greek buildings and acoustics, with applications to modern conditions.

_Eichhorn, A._ “Der Akustische Masstab für die Projectbearbeitung
Grosser Innen Raüme.” Published by Schuster and Bufleb, Berlin, 1899. A
continuation of the previous work.

_Exner, S._ “Uber die Akustik von Hörsälen und ein Instrument,
sie zu bestimmen.” Zeitschrift des Osterreichischen Ingenieur und
Architekten-Vereines, Vol. LVII, p. 141, March, 1905. Indicates his
opinion of good acoustical properties in a hall. Gives experimental
determination of reverberation.

_Fournier, Lucien._ “The Suppression of Echoes.” La Nature (Paris),
April 24, 1909. English translation given in “The Literary Digest,” New
York, May 29, 1909, p. 924. An account of the experiments of Gustav
Lyon in investigating the echoes in Trocadero Hall in Paris.

_Franklin, W. S._ “Derivation of Equation of Decaying Sound in a Room
and Definition of Open Window Equivalent of Absorbing Power.” Physical
Review, Vol. 16, pp. 372–374, 1903. A theoretical development of the
formula found experimentally by Sabine.

_Haege._ “Bemerkungen über Akustik.” Zeitschrift für Baumesen, Vol. IX,
pp. 582–594, 1859.

_Henry, Joseph._ “Acoustics Applied to Public Buildings,” Smithsonian
Report, 1856, p. 221.

_Hoyt, J. T. N._ “The Acoustics of the Hill Memorial Hall,” American
Architect, Vol. CIV, pp. 50–53, August 6, 1913. Discusses the design of
the hall and indicates how it fulfills his ideas of good acoustics.

_Hutton, W. R._ “Architectural Acoustics; Hall of Representatives,
U. S. Capitol, 1853.” Engineering Record, Vol. 42, p. 377, 1900. A
discussion of the cure of the faulty acoustics in the U. S. Hall of
Representatives.

_Jacques, W. W._ “Effect of the Motion of the Air Within an Auditorium
Upon Its Acoustical Qualities.” Philosophical Magazine (5), Vol. 7,
p. III, 1879. A record of experiments in the Baltimore Academy of
Music showing that the ventilating current had a marked action on the
acoustics.

_Jager, S._ “Zur Theorie des Nachhals,” Sitzungsberichten der Kaiserl.
Akademie der Wissenschaften in Wien. Matem.-naturw. Klasse; Bd. CXX,
Abt. Ha, Mai, 1911. An important paper giving a theoretical development
of Sabine’s formula showing the factors that enter into the constants.
Considers also the case of the reflection of sound from a thin wall and
also the case when it encounters a porous material such as a curtain.

_Lamb, Horace._ “The Dynamical Theory of Sound.” Published by Edward
Arnold, London, 1910. A more elementary treatment than Rayleigh’s
“Theory of Sound.”

_Marage._ “Qualites acoustiques de certaines sailes pour la voix
parlée.” Comptes Rendus, Vol. 142, p. 878, 1906. An investigation of
the acoustical properties of six halls in Paris.

_Norton, C. L._ “Soundproof Partitions.” Insurance Engineering, Vol.
4, p. 180, 1902. An account of experimental tests of the soundproof
qualities of materials that are also fireproof.

_Orth, A._ “Die Akustik Grosser Raüme mit Speciallem Bezug auf
Kirchen.” Zeitschrift für Bauwesen. Also reprint by Ernst and Korn,
Berlin, 1872. Assumes that sound waves behave like light waves.
Discusses, with detailed drawings, the paths of sound in the Zion
Church in Berlin and the Nicolai Church in Potsdam. Also gives his
opinion of the effect of surfaces and materials on sound.

_Rayleigh, Lord._ “Theory of Sound.” Two volumes, Macmillan, 1896.
The unsurpassed classic in the subject of acoustics. References to
architectural acoustics as follows: “Whispering Galleries,” Vol. II, §
287. “Passage of Sound Through Fabrics,” Vol. II, p. 311. “Resonance in
Buildings,” Vol. II, § 252.

_Sabine, Wallace C._ “Architectural Acoustics.” Engineering Record,
1900, Vol. 1, pp. 349, 376, 400, 426, 450, 477, 503. Published also
in book form and in American Architect, Vol. 68, 1900, pp. 3, 19, 35,
43, 59, 75, 83. An important series of articles giving the relation
between the time of reverberation in a room, the volume of the room,
and absorbing materials present. Gives table of absorbing powers
of substances, so that an architect can calculate in advance of
construction what the time of reverberation will be.

_Sabine, W. C._ “Architectural Acoustics,” Proc. of the Amer. Acad.
of Arts and Sciences, Vol. XLII, No. 2, June, 1906. A continuation of
the previous work, showing the accuracy of musical taste in regard to
architectural acoustics and also the variation in reverberation with
variation in pitch.

_Sabine, W. C._ “Architectural Acoustics,” Engineering Record, Vol. 61,
pp. 779–781, June 18, 1910. Discusses the case of flow of air in a room
and its effect on the acoustics. Concludes that the usual ventilation
system in a hall has very little effect.

_Sabine, W. C._ “Architectural Acoustics: The Correction of Acoustical
Difficulties.” The Architectural Quarterly of Harvard University,
March, 1912, pp. 3–23. An account of the cures of the acoustical
difficulties of a number of audience rooms, also a description of
further experiments on the absorbing power of different materials.

_Sabine, W. C._ “Theater Acoustics.” American Architect, Vol. CIV, pp.
257–279, December 31, 1913. Describes theater with model acoustics.
Discusses behavior of sound in a room and shows photographs of sound
waves in miniature rooms.

_Sabine, W. C._ “Architectural Acoustics. Building Material and
Musical Pitch.” The Brickbuilder, Vol. 23, pp. 1–6, January, 1914. A
continuation of previous work, describing absorbing powers of different
materials.

_Sharpe, H. J._ “Reflection of Sound at a Paraboloid.” Camb. Phil. Soc.
Proc., Vol. 15, pp. 190–197, 1909.

_Stewart, G. W._ “Architectural Acoustics.” Sibley Journal of
Engineering, May, 1903. Published by Cornell University, Ithaca, N. Y.
An account of an investigation leading to the cure of the acoustics of
Sibley Auditorium.

_Sturmhöfel, A._ “Akustik des Baumeisters.” Published by Schuster
and Bufleb, Berlin, 1894. An 87-page pamphlet on the acoustics of
rooms. Discusses effects of relief work in rooms on sound. Account of
experimental work. References to auditoriums.

_Tallant, Hugh._ “Hints on Architectural Acoustics.” The Brickbuilder,
Vol. 19, 1910, pp. 111, 155, 199, 243, 265. A series of articles
giving an exposition of the principles of the subject with practical
applications.

_Tallant, Hugh._ “Acoustical Design in the Hill Memorial Auditorium,
University of Michigan.” The Brickbuilder, Vol. XXII, p. 169, August,
1913. See also plates 113, 114, 115. A discussion of the acoustical
results obtained in this auditorium, a special feature being the action
of a huge parabolic reflecting wall surface over the stage.

_Tallant, Hugh._ “Architectural Acoustics. The Effect of a Speaker’s
Voice in Different Directions.” The Brickbuilder, Vol. 22, p. 225,
October, 1913.

_Taylor, H. O._ “A Direct Method of Finding the Value of Materials as
Sound Absorbers.” Physical Review, Vol. 2 (2), p. 270, October, 1913.

_Tufts, F. L._ “Transmission of Sound Through Porous Materials.” Amer.
Journal of Science, Vol. II, p. 357, 1901. Experimental work leading to
the conclusion that sound is transmitted through porous materials in
the same proportion that a current of air is.

_Watson, F. R._ “Echoes in an Auditorium.” Physical Review, Vol. 32,
p. 231, 1911. An abstract giving an account of the experiments in the
auditorium at the University of Illinois.

_Watson, F. R._ “Inefficiency of Wires as a Means of Curing Defective
Acoustics of Auditoriums.” Science, Vol. 35, p. 833, 1912.

_Watson, F. R._ “The Use of Sounding Boards in an Auditorium.” Physical
Review, Vol. 1 (2), p. 241, 1913. Also a more complete article in The
Brickbuilder, June, 1913.

_Watson, F. R._ “Air Currents and the Acoustics of Auditoriums.”
Engineering Record, Vol. 67, p. 265, 1913. A detailed account giving
theory and experimental work, with application to ventilating systems
in auditoriums.

_Watson, F. R._ “Acoustical Effect of Fireproofed Cotton-Flannel Sound
Absorbers.” Engineering News, Vol. 71, p. 261, January 29, 1914.
Results of experiments showing that cotton-flannel has practically the
same absorbing power after fireproofing as before.

_Weisbach, F._ “Versuche über Schalldurchlassigkeit, Schallreflexion
und Schallabsorbtion.” Annalen der Physik, Vol. 33, p. 763, 1910.

_Williams, W. M._ “Echo in Albert Hall.” Nature, Vol. 3, p. 469,
1870–71. Observations on the shape of Albert Hall in London and the
echoes set up.

_Editorial Notice._ “The Dresden Laboratory for Architectural
Acoustics.” American Architect, Vol. 102, p. 137, October 16, 1912.
States that a laboratory of applied acoustics is authorized in the
Dresden (Germany) Technische Hochschule, and that expert advice will
be furnished architects and others regarding problems of acoustics of
auditoriums.



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FOOTNOTES


  [1] “Theory of Sound,” Vol. II, p. 316.

  [2] “Theory of Sound,” Vol. II, § 351.

  [3] “Dynamical Theory of Sound,” p. 196.

  [4] “Theory of Sound,” p. 333.

  [5] “Architectural Acoustics.” A series of articles in the
      Engineering Record, 1900; also the American Architect, 1900.

  [6] “Architectural Acoustics,” Proc. of Amer. Acad. of Arts and
      Sciences. Vol. 42, pp. 49–84, 1906.

  [7] G. W. Stewart. “Architectural Acoustics,” Sibley Journal of
      Engineering, May, 1903. Published by Cornell University, Ithaca,
      N. Y.

  [8] “Qualités acoustiques de certaines salles pour la voix parlée.”
      Comptes Rendus, 142, 878, 1906.

  [9] W. S. Franklin. “Derivation of Equation of Decaying Sound in
      a Room and Definition of Open Window Equivalent of Absorbing
      Power.” Physical Review, Vol. 16, pp. 372–374, 1903.

 [10] G. Jäger. “Zur Theorie des Nachhalls.” Sitzungsberichte der
      Kaiserliche Akad. der Wissenschaften in Wien, Math-naturw.
      Klasse; Bd. CXX. Abt. 11 a. Mai, 1911.

 [11] Science, Vol. 35, p. 833, 1912.

 [12] Arch. Quarterly of Harvard University, March, 1912.

 [13] Osborne Reynolds. Proc. of Royal Soc., Vol. XXII, p. 531, 1874.

 [14] Joseph Henry, “Report of the Lighthouse Board of the United
      States for the year 1874.”

      J. Tyndall, Phil. Trans., 1874.

 [15] Sabine, Engineering Record, Vol. 61, p. 779, 1910. Watson,
      Engineering Record, Vol. 67, p. 265, 1913.

 [16] Sabine and Watson. Ibid.

 [17] La Nature (Paris), April 24, 1909.

 [18] Rayleigh “Theory of Sound,” Vol. II, § 283.

 [19] Rayleigh, ibid, 283.



Transcriber’s Notes


Punctuation, hyphenation, and spelling of English words were made
consistent when a predominant preference was found in the original
book; otherwise they were not changed. The spellings of non-English
words were not changed.

Simple typographical errors were corrected; unbalanced quotation
marks were remedied when the change was obvious, and otherwise left
unbalanced.

Illustrations in this eBook have been positioned between paragraphs
and outside quotations. In versions of this eBook that support
hyperlinks, the page references in the List of Illustrations lead to
the corresponding illustrations.

Footnotes have been sequentially numbered and placed together at the
end of the book.



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