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.