Introduction to Acoustics

is of key importance in rooms where an audience is listening
to a performance or lecture. In this type of room,
it is desirable that all audience members hear the sound
not only clearly, but without preference to seating location.
Without an electronic sound system, this can
only be accomplished by reflections off side walls and
ceilings. Discrete echoes can be eliminated by avoiding
smooth, flat reflective surfaces and by having irregular
and convex surfaces to diffuse the sound evenly throughout
the audience. For smaller rooms such as recording
studios that require diffusion, commercially available
sound-diffusing panels called quadratic residue diffusers
are available. These panels can also be used for larger
spaces, as well as irregularly shaped surfaces.
Concave reflective surfaces focus sound in certain
areas and defocus sound from others, causing hot spots
where sound is concentrated and dead spots where sound
cannot be heard. Concave reflective surfaces should be
avoided for this reason. If aesthetics dictate the need
for a concave surface, it would be best to install an
absorptive or diffusive surface (as needed) and cover it
with acoustically transparent fabric in the concave shape.
Reflective rear walls in auditoriums are notorious
for generating echoes because of their associated large
sound travel path differences. For this reason, reflective
surfaces should be avoided for rear walls. Reflective surfaces
are beneficial, especially for concert halls, when
they are close to the stage and along side walls. Reflective
surfaces close to the stage assist in several ways,
by sending sound into the audience rather than allowing
it to be lost behind the stage and by enhancing the
sound through lateral reflections off side walls to spread
the sound more evenly throughout an audience. Another
benefit of reflective surfaces near the stage is that they
permit the performers to hear each other, something that
is critical to concert performances. These so-called early
reflections are usually generated by shells on the stage
or by hanging reflective panels.
11.1.6 Sound Insulation
The description of the insulation of sound is similar in
many ways to the description of the absorption of sound.
As with absorption, there is a transmission coefficient
that ranges from the ideal limits of 0 to 1. The transmission
coefficient, denoted by the Greek letter τ,isthe
unitless ratio of transmitted to incident sound energy.
Unlike the absorption coefficient, however, the limit of
τ = 1 is possible in practice since a transmission coefficient
of 1 implies that all of the sound energy is
transmitted through a partition. This would be the case
TL
Building Acoustics 11.1 Room Acoustics 395
Stiffness Resonance Mass law Coincidence
6dB increase per doubling
of mass and frequency
Vibration isolation
Heavy damping
Light damping
f critical
Frequency
Fig. 11.14 General characteristics of the transmission loss
spectrum
for an open window or door, where the sound energy
has no obstruction to its path. The other extreme of
τ = 0 (implying no sound transmission), however, is not
a practical value since some sound will always transmit
through a partition.
Unlike absorption, the principal descriptor for sound
insulation is a decibel level based on the transmission
coefficient. This value is known as the transmission loss
(TL), and is based on the following equation:
TL = 10 · log(1/τ) . (11.6)
The transmission loss can be loosely defined as the
amount of sound reduced by a partition between a sound
source and a listener. The complete sound reduction of
a partition between two rooms also takes into account
the absorptive characteristics of the listener’s room, as
follows:
SPLS − SPLL = TL + 10 · log(AL/S) , (11.7)
where SPLS is the average sound pressure level in the
room enclosing the sound source, SPLL is the average
sound pressure level in the adjacent listener’s room, AL
is the total absorption in the listener’s room, TL is the
transmission loss of the partition between the two rooms,
and S is the surface area of the partition between the
two rooms. Note that TL is the quantity that is typically
reported in manufacturers’ literature since it is measured
in a laboratory independent of the installation.
Since the logarithm of 1 is 0, the condition in which
the transmission coefficient is 1 translates to a TL of
0 dB. This concurs with the notion that an open air space
in a wall allows the free passage of sound. Although an
open air space itself would have a TL value of 0 dB
associated with it, a wall with an open air space in it
Part C 11.1