Small Room Acoustics 135should also be applied to all the modes, the axial,
tangential, and oblique. There are many excellent tools
for calculating modal distribution.6.7 The Question of ReverberationW.C. Sabine, who first formulated the equation to calcu-
late reverberation time, described reverberation in this
way: “reverberation results in a mass of sound filling
the whole room and incapable of analysis into its
distinct reflections.”^10 What Sabine was saying,
although he did not use these terms, was that for true
reverberation to exist, there needs to be a homogenous
and isotropic sound field. Usually such conditions are
approached in physically large rooms that do not
contain much absorption. Unfortunately the term rever-
beration is popularly understood to be equivalent to
decay. Does reverberation time refer to the decay of a
well-established, totally homogenous, diffuse sound
field that exhibits no net energy flow due to the richness
of the reflections present or does reverberation time
refer to the decay of any sound in a room no matter
what the nature of the sound is, even if it is not diffuse?
To some extent, this is a question of semantics. It is
interesting to note that maybe Sabine himself perhaps
anticipated the confusion that would eventually arise
because in the same paper he wrote:The word “resonance” has been used loosely as
synonymous with “reverberation” and even with
“echo” and is so given in some of the more
voluminous but less exact popular dictionaries.
In scientific literature the term has received a
very definite and precise application to the
phenomenon where ever it may occur. A word
having this significance is necessary; and it is
very desirable that the term should not, even
popularly, by meaning many things, cease to
mean anything exactly.^11It is the opinion of this author that this is precisely
where we find ourselves today. Without a rigorous defi-
nition and application of the concept of reverberation,
we are left with something which ceases to mean
anything exactly.
When Sabine first measured the decay of the rever-
beration in Fogg Lecture Hall at Harvard, he did it with
an organ pipe and a stopwatch. He had no way of exam-
ining the fine detail of the reflections or any of the
components of the sound field, nor was he initially
looking at decay as a function of frequency. (Later on he
looked at decay as a function of frequency, but never
connected this to room size or shape.) He could only
measure the decay rate of the 513 Hz pipe he was using.
The volume of the lecture hall was approximately
96,700 ft^3.^13 The room was large enough that 512 Hz
was not going to energize any of the normal room
modes. Since there was virtually no absorption in the
room whatsoever, it is likely that Sabine was measuring
a truly diffuse sound field. It is interesting to note that in
Sabine’s early papers he rarely mentions the dimensions
other than the volume of the rooms he was working in.
He was convinced that it was the volume of the room
that was important. The mean free path was also central
to his thesis. The MFP is defined as the average
distance a given sound wave travels in a room between
reflections.^14 The equation for finding the mean free
path is(6-5)where,
V is the volume of the room,
S is the total surface area.Consider a small room with dimensions of
12ft×16ft×8ft high (3.66m×4.88m×2.44m).
This room will have a volume of 1536 ft^3 (43.5 m^3 ) and
a total surface area of 832 ft^2 (77.3 m^2 ). Putting these
numbers into Eq. 6-5 yields a result of a MFP of about
7.38 ft. At the average speed of sound (1130 ft/s or
344 m/s) this distance will be covered in 0.00553 s or
5.53 ms. It is generally accepted that in small rooms,
after approximately four to six bounces, a sound wave
will have lost most of its energy to the reflecting
surfaces and will become so diffuse as to be indistin-
guishable from the noise floor. This of course depends
on the amount of absorption in the room. In very
absorptive rooms there may not be even two bounces. In
very live hard rooms a wave may bounce more than six
times. In this room a single wave will take only 32.6 ms
to bounce five times and be gone. Compare this with a
large room. Consider a room that is 200 ft long by
150 ft wide with a 40 ft ceiling (61 m × 45.7 m
12.2 m). This room will have a MFP of 54.5 ft
(16.61 m). It will take 241.3 ms for a single wave to
bounce five times and dissipate.
Sabine was not interested in the shape of the room or
even in the distribution of the absorptive material. He
focused on the statistical nature of the diffuse sound
field and on the rate of decay. Other researchers looked
at similar issues eventually dividing the time domain
performance into smaller and smaller regions and exam-
ining their contributions to the subjective performance
of rooms.MFP^4 V
S------ -=