Introduction to Acoustics

selected). A distance different from 10 m can be used,
if a correction for the distance attenuation is applied as
well.
The expected value of G according to diffuse field
theory becomes a function of T as well as of the room
volume, V:
Gexp = 10 log 10
Acoustics in Halls for Speech and Music 9.3 Subjective and Objective Room Acoustic Parameters 309
� �
T
+ 45 dB . (9.12)
V
The subjective difference limen for G is about 1.0dB.
The definition of G is illustrated in Fig. 9.7.
9.3.4 Measures of Spaciousness
Spaciousness is the feeling that the sound is arriving
from many different directions in contrast to a monophonic
impression of all sound reaching the listener
through a narrow opening. It is now clear that there are
two aspects of spaciousness, both of which are attractive,
particularly when listening to music:
• apparent source width (ASW): the impression that
the sound image is wider than the visual, physical
extent of the source(s) on stage. This should not be
confused with localization errors, which of course
should be avoided.
and
• listener envelopment (LEV): the impression of being
inside and surrounded by the reverberant sound field
in the room.
Both aspects have been found to be dependent on
the direction of incidence of the impulse response reflections.
When a larger portion of the early reflection
energy (up to about 80 ms) arrives from lateral directions
(from the sides) the ASW increases. When the level of
the late, lateral reflections is high, strong LEV results.
The lateral components of the impulse response energy
can be recorded using a figure-of-eight microphone
with the sensitive axis held horizontal and perpendicular
to the direction towards the sound source (so that
the source lies in the deaf plane of the microphone). For
measurement of the lateral energy fraction (LEF), the
early part (up to 80 ms) of this lateral sound energy is
compared with the energy of the direct sound plus all
early reflections picked up by an ordinary omnidirectional
microphone:
LEF =
�
t=80 ms
t=5ms
h 2 l (t)dt
� t=80 ms
�
t=0ms
h 2 (t)dt , (9.13)
G = 10log10
h2 ¥
(t)dt
ò
ò
0
t dir
0
h 2 10m(t)dt
h 2 (t)
*
10m
t (ms)
Fig. 9.7 The definition of strength G: the total energy in the impulse
response measured relative to the direct sound level at 10 m distance
from the source
where hl is the impulse response pressure recorded with
a figure-of-eight microphone, whereas h is captured
through the (usual) omnidirectional microphone.
It is mainly the energy at low and mid frequencies
that contribute to the spaciousness. Consequently,
LEF is normally averaged over the four octaves
125–1000 Hz. The higher the value of LEF, the wider
the ASW. The literature contains many data on LEF
values in different, existing concert halls.
LEF does not have an expected value related to T.In
a completely diffuse field, LEF would be constant with
a value of 0.33, which is higher than that normally found
in real halls. The subjective difference limen for LEF is
about 5%.
The definition of LEF is illustrated in Fig. 9.8.
The ASW aspect of spaciousness is not only dependent
on the ratio between early lateral and total early
Spaciousness
Lateral energy fraction
LEF =
t = 80 ms
2
ò hl (t)dt
t = 5ms
t = 80 ms
ò
t = 0 ms
h 2 (t)dt
h 2 (t) – fig. of eight microphone
5ms 80ms
h 2 (t) – Omni microphone
5ms 80ms
t (ms)
t (ms)
Fig. 9.8 The definition of lateral energy fraction LEF: the ratio
between early reflection energy arriving from the sides and total
early energy
Part C 9.3